A 1993 mustang gt with 5.0 manual transmission should be an A9L bin code. These were once highly sought after as the best of the EEC4. There are some capacitors in them that are starting to fail, now. 21 yrs is a long time for a capacitor to last. They are not hard to replace, but require soldering skills. Some experts recommend changing them out, before they fail, as when they fail they can cause other damage. Other than that, they are bullet proof.
You can chip these ECUs and have full access to change anything in the tuning parameters. Moates sell a QH (quarter horse) chip that gives amazing access. Moates.net has a write up with pictures on how to change out the capacitors. The do it yourself route will run you about $500 for chips and software, or you can take it to a dyno tuner that will cost about the same. Of course you do not need to do anything until you modify the engine. If you chip the EEC4 it can be tuned to run any engine.
An aftermarket ECU that will give you the access that the maotes chip gives you will run $2000 - $3000.
Here is a link to Moates, if you are ever interested
https://www.moates.net/
PS.
When the Key is on the ECU is required to turn the fuel pump off. If the ECU becomes corrupted, the fuel pump will run continuously with the key turned on. I doubt the ECU is your problem. A relay or fuse is much more likely.