When you say the battery is good, did you have it load tested (many parts stores will do that for you). If the battery fails the load test you can try to slowly and fully charge the battery. Replace the battery if it can't take a full charge, or if it still fails the load test after fully recharging it. If the battery is capable of being charged, and passes the load test you can reinstall it and check the charging system. Testing the charging system is fairly easy on a Ford or Lincoln Mercury. There are several good YouTube videos showing how to perform a simple test on these charing systems. But to relly check the charging system out can take some costly equipment and additional techniques beyond the scope of many of the YouTube videos I have seen. But, some simple tests as shown in the YouTube videos I have seen are a good place to start.
The next thing I would suggest is for you to make certain there is an engine to body ground strap in place and connected properly. I have seen a f lot of cases where someone has done some major engine work, and simply forgot to reconnect the ground strap between the engine and body. On some vehicles, including early Mustangs, there is a body ground terminal on the battery ground cable itself, as opposed to a separate ground strap. But, somewhere there needs to be a solid connection made with a high enough capacity to handle the amperage needed for the starter motor's ground current, and other electrical devices being used.
After checking the ground strap/connection you can bypass the Ignition Switch by jumping the starter relay to see if it is working properly. o jump the Starter Relay you can sort the large positive battery cable connected to the Start Relay to the Start Relay's smaller "S" Terminal. Doing that will cause the Starter Relay to crank the engine over, For a description of the Starter Relay terminals watch this video:
If the Started Relay is making a loud clicking sound, but no cranking the Starter Relay may be bad, or the cable leading from the relay to the starter is bad, or there is a bad connection between the Starter Relay and the Starter Motor, or there is a bad ground connection between the engine and the body (ground strap is loose or missing), or the Starter Motor itself is bad.
One place I see connections go bad is simply between the battery posts and the inside surface of the battery cable lugs themselves. On many occasions simply using a battery terminal brush on those contact surfaces fixes a slow or no crank situation. There are a few nice YouTube videos showing how to use battery terminal brush. Here is one of them:
If turning the ignition key to the Start/Crank position does not cause the Starter Relay to click or engage the Starter, there is a problem in the Ignition Switch or related circuitry. It could be a simple adjustment needed of the Neutral Safety Switch, or something a bit deeper (Ignition Switch or he related circuitry. Attached are some wiring schematic PDF files for a 1973 Mustang's starting circuit (and some other nearby circuits as well).