Check Engine Light on and Car over heating

I hate to say it but it is either a head gasket or air in system and was not filled all the way. check to make sure coolant is full then once it is run car and shut down let cool and check again in degas bottle. This guide will help us get the codes

https://www.2carpros.com/articles/ford-lincoln-mercury-obd1-1995-and-earlier-diagnostic-trouble-code-definition-and-retrieval

Please run down these guides and report back.

Because it has to deal with air in system so you should do what I said in first reply to see if it goes out.

Fuel pump will cause a no start in most cases, bad coil will turn a check engine light on and will cause engine to run rough and hesitate , also a bad spark plug or the need to a tune up
Codes should indicate to the the reason for a check engine light

Fuel pump failure and low fuel pressure should not effect only one cylinder
As in your case only cylinder # 4 was the troubled one
Check injector
Check coil
Check and do a compression test

The connector for the test is under the hood, on the right side, near the firewall. It is usually in a black plastic protector that has EEV TEST printed on it. To read the codes, you will need either a Ford STAR tester or an OBD-1 tester with Ford adapter cable. You can also ground the STI pin of the test connector and get the code(s) flashed out on the "CHECK ENGINE" light

Let me know what codes you get, and I can help you further.

Which engine warning light? Oil, temp, check engine? If it is check engine, have the PCM scanned for codes. Any other warnings check engine fluids, oil, coolant

The Engine Computer detected a problem, set a diagnostic fault code, and turned the Check Engine light on to tell you. Many auto parts stores will read the codes for you for free. Those will indicate the circuit or system that needs further diagnosis.

There are well over 1000 potential fault codes so there's no way to guess what it is. You can make some generalizations by the way the Check Engine light acts. About half of the codes won't even turn the light on. The light must turn on when the problem detected could adversely affect emissions. If the light turns off while you're driving, the problem went away for now and those are the least serious. If the problem stops acting up while you're driving but it was a little more serious, the light will stay "latched" on until you stop and restart the engine, like you described. If it's still more serious the light will be on any time you run the engine even if the problem hasn't acted up in a while. For really serious problems the light will flash while you're driving. That's when you must stop the engine right away to prevent overheating the catalytic converter and damaging it. That is caused by too much raw fuel going into the exhaust system.

I would suggest recheck work area for a lose or disconnected plug and or a wire
checking for codes would be my next step as codes would help in pin pointing what is happening and the reason for check engine light to be on
disconnecting battery would reset all
good luck let me know

Take it to a nationally recognized parts store and have them scan the codes and reset. (Also, you can try disconnecting the battery for about 10 minutes to see if that will do it. If it doesn't, it will require a scanner.)

This is an intermittent fault. Could be a sensor going faulty or a wiring problem. Untill the light stays on and gives a fault code it will be difficult to trace?