It's a 73 mustang.
Bought the car few weeks ago as is and looked into this today.
Runs rought at idle (likes to die when cold), chokes and at times stals when starting to accelerate from the dead stop (auto). Engine runs fairly smooth while driving.
Lookes like it has Petronix Flamethrower with Igniter 3, while rest of the ignition seems to be stock.
Yeah, I have more to share with you, re: the "Runs rough at idle (likes to die when cold), chokes and at times stalls when starting to accelerate from the dead stop (auto). Engine runs fairly smooth while driving." The runs rough at idle and the choking and stalling when accelerating condition tells me you are running into a carburetor issue, or at least something that is causing you to run a bit lean when you need a richer Air/Fuel ratio (cold engine). From your member info I see you are running a 2v carburetor, and I am assuming it is an Autolite 2100. If so, that is a good thing as they are simple to work on, fairly easy to adjust, and also easy to rebuild when needed. We also have a 2100 on our 73 Mustang Convertible's 302 engine, and I had to work on it recently, as it was causing a slight hesitation on light acceleration. Before I tore into the carburetor I first disconnected the vacuum line to the EGR valve (temporarily, it was connected again) to make sure the EGR valve opening off idle was not causing the hesitation - the condition remained unchanged, so it was not the EGR valve causing the problem. With the air cleaner off I watched down the venturi throats as I opened the throttle to make certain the accelerator pump was sending "adequate" fuel out the acceleration pump discharge nozzles. That also looked good.
A quick aside, I purposely said "sending 'adequate' fuel out the ... discharge nozzles" for a reason. Story time... Years ago, working as a tech at a Lincoln dealership, a customer with a new Mercury Monarch (Ford Granada) came in saying he had a hesitation on acceleration. I took the car out and he was right, but it was not as bad as most cars when an accelerator pump was having problems. I suspected the EGR valve, but as with our car unplugging it (temporarily) did not help. When I looked down the venturis and opened the throttle only one discharge nozzle was squirting fuel in an amount I was expecting. The other was dribbling (on a new car). I took the accelerator pump and fuel pickup assembly off and found some brass cuttings stuck in the one discharge nozzle(!). The customer was a young guy who was obviously tasting success in his business, so I told him what I found, and if he wanted I could make extra sure he had decent acceleration beyond just removing the machine cutting out of the nozzle, but it may cause his fuel mileage to drop a little - hardly noticeable. He was all for more pep, so I used a jeweler's drill bit and hand vise, and not only cleared the one accelerator brass outlet from the one nozzle, but I used a slightly larger drill bit to make both nozzles just a very tiny bit larger in diameter - it does not take much to effect a change in performance). I went out on a test drive, with him, after wrapping it up. Wow! He was impressed, especially once I changed places with him and let him drive us back to the dealership. Ever since then I have made it a habit of looking at the accelerator pump fuel discharge whenever I had a car come in, complaint or not.
Anyway, back to our 2100 project... With the accelerator pump looking like it was working good, the EGR not causing the hesitation, and the distributor vacuum advance system working properly, I felt the only other two possibilities were the air breaks for the venturi fuel pickup tubes were plugged (very unlikely), or the fuel float level in the fuel bowl was too low. Well, here is "the twist" in this situation...
This particular vert was literally barn stored over 30 years, after the 2nd owner had gotten very ill, and later passed away. He had purchased the vert when it was virtually new, as the original owner traded it in for a 4x4 when he retired soon after buying the vert. The 3rd owner, a Mustang enthusiast, came across it many years later, in a barn, and purchased it. At the time the Mustang only had about 13,000 original miles on it (circa 2007). When we purchased it in mid 2019 it only had just over 19,000 original miles on it (see attached image file)! The engine had been running well when we first got it, and later when the hesitation became evident I did not feel enough time had passed to have the air breaks in the venturi fuel pickup tubes to get plugged - but it was a lot of years. But, it also seems unlikely the float level would have been too low for what was essentially an almost new car, hardly used. No matter, the carb was coming off.
Upon removing the carb I noted the passenger front mounting nut was finger tight, at best. The other three nuts felt tight as I removed them. I looked at the gasket between the base of the carb, and the intake manifold. It was an extra thick gasket that was intended to prevent too much engine heat from getting to the carburetor fuel bowl and boil the fuel. The part of the gasket nearest the loose nut never crimped properly, so that meant we had at least a nominal vacuum leak. Enough to cause the idle mixture adjustment screws to have been run out by 4 turns, more than I would have expected (usually 2 3/4 - 3 1/4 turns). But, not enough of a leak to explain the hesitation. The air breaks for the venturi pickup fuel tubes were not plugged, the air inlet and venturi clusters looked very clean - what I would have expected for a fairly low mileage engine and carburetor. I then removed the top cover, and pressed on the fuel float tang over the fuel needle/valve inlet. Ah ha! I found the problem. The float was set about 1/4" too low, may be more. But, how? Why? It was not likely it came that way from the factory, and I had rebuilt enough of those 2100s back "in the day" to know their float levels were pretty much dead on from the factory. Then, I figured it must have been rebuilt for some reason, most likely a leaking or ruptured Power Valve, and the float was adjusted too low - maybe by accident, maybe "on purpose." But, why would anyone set it too low? Well, back "in the day" there were some folks who intentionally set fuel float levels a little on the low side to allegedly get better fuel mileage as it causes the carb to produce a leaner Air/Fuel ratio. But, this was lower than that kind of malarky. No matter...
I went ahead and rebuilt the carburetor, and found the Power Valve had been double gasketed. Definitely "someone" had it apart previously, and whoever it was used two gaskets (often two gaskets of slightly different shapes are provided in the rebuild kits) instead of just choosing the one that best fit where the Power Valve fuel channels were located (often two gaskets of slightly different shape are provided in the rebuild kits). So I installed the new Power Valve, using only one gasket, cleaned out the various air and fuel channels, replaced the fuel inlet needle and seat, and adjusted the float to its proper level (after shaking it to see if any fuel was leaking into it - brass float). After I reassembled the carb, it fired up immediately, and only required me to lean out the idle mixture screws a little bit, now that the base plate vacuum leak was fixed when I properly tightened down all for mounting nuts. On the test drive, the carburetor performed perfectly, the hesitation upon acceleration (light or heavy) was gone.
I (of course) had Lynda do a video recording of the carb rebuild and adjustment processes. It is a long video (over 3 hours), but if you have never rebuilt a 2100 before I think you will find some good info in it. You can fast forward past any boring parts if you like. I also have two other related videos. One shows how to adjust the cold high idle speed cam and screw, the Throttle Position Solenoid (TPS), the idle Air/Fuel mixture screws, and the Base Idle speed (TPS off) setting. Another shows how I corrected a fuel leak where the fuel filter is screwed into the carb housing, as "someone" previously screwed the filter in far too deeply, which caused me to have to deal with a fuel leak.
I hope you find the videos useful. I do feel your hesitation is due to an accelerator pump or related issue, but without seeing the car it is hard to tell for sure. But, the only other thing (besides an EGR valve that open too aggressively, or a too low fuel float level) that can cause a hesitation on acceleration is a ruptured or leaking distributor vacuum advance diaphragm, and that causes more of a sluggish performance issue on acceleration than a true carburetor induced hesitation or "bog." And, of course, I have some videos that show how to test a distributor vacuum advance diaphragm, and how to to test to make certain ported vacuum is making it to the diaphragm to begin with. You may need to skip around a it to find the vacuum advance diaphragm and ported vacuum testing parts, as I cover a few things in the following videos. But, if you end up watching more than what you need you may just learn something else that will help you someday.
I hope all that helps you with the hesitation issue you are having.