The electrical systems on cars suck, lol. It is so difficult to get to them is big issue. If you have lots of issues it is probably best to remove the entire dash as an assembly. Sounds bad but not actually. Only like 8 bolts that hold it in. Just getting to a few of them is tough. One is hidden under the steering column which has to be dropped to get dash out.
You remove instrument cluster after dropping column. I would remove the front seats before you start and console also.
Once the instruments out remove the upper dash and pad. Then you can get to the bolts on the top. 73 models have a couple extra phillips screws in center area.
You have to unplug all the connections in both kick pad areas. Take the bolt loose in the center of the fuse box and get the dash harness unplugged from the under hood harness.
We do have a member, Midlife, that restores wire harness. He is shut down right now due to home repairs from storm damage.
You can attempt some on your own. Get you a tube of permatex electrical grease. You will have to spend hours and days cleaning every connection with steel wool wire brushes etc. to get any corrosion off. Then when you make a connection brush on a little of the electrical grease.
Grounds are very important. There is a ground connection in the middle of the dash that goes to the cowl area wish I had a pic but lost them.
With the dash out the snowball keeps growing. Best time ever to remove the heater box and replace the heater core and all the foam pieces on the doors inside. Do research on rebuild West Coast Cougar has great video on their site. Test out your heater AC fan and the vacuum controls. A brake bleeder will test the vacuum motors.
The tail lights are a real pain also. Getting all the sockets clean, contacts clean, test each bulb and clean the bases and contact points. Apply the electrical grease when you go back together. Due to the plastic tail light housing each light has it's own ground which needs to be spotless and add the grease. Test the lights on bench without being hooked to main harness.
Again the snowball grows. Good time to take the tail lights housings out and clean up around the seal area where the water leaks into the trunk rusting it out.
Daniel Carpenter makes new tail light lens and the aluminum trim just for 73 you have to mask and paint for 71 - 72. He also makes a much better seal for the housings. I also put a bead of 3-M strip caulk around the opening for the light.
With the lens off of the tail light housing you will see why the lights look dim when they do work. The plastic turns yellow and flakes off over time. I blast mine with walnut shells and put a coat of the Krylon Fusion Satin paint on matches factory finish perfect. Picture shows the can and front parking light off 73 I did.
The headlight and parking lights along with side marker lights all need the same treatment, clean clean clean, electrical grease and back in. Remove any paint from areas where ground connections go like on the radiator support.
Clean the ground connections from the battery one behind the voltage regulator, one on engine block. I actually add an extra ground strap from engine to chassis just to make sure.
I did two cars in past couple years and the electrical is the worst part to me.
The instrument cluster has a printed circuit. There is a diagram one member made of what each connection is. Would have to search for it I lost my copy. I have found that an eraser is good for cleaning the printed circuit to remove any contamination. Clean each bulb socket, connections and the bulb itself. Test each bulb outside the socket and then in the socket before putting back into the cluster.
With the harness and dash out go over the wiring and fix any bare spots. If someone has cut be sure you splice back using solder not just twisting and tape. They make a special non stick tape you wrap the harness with can get from Mustang supply houses.
There is no simple way to get in there and fix it wish there was.