Engine backfire's when you let off gas but idle's fine

Question edited for clarity and remove abbreviations.
Question moved to model category.

Check the relay.

https://www.google.com/search?q=1988+mitsubishi+mighty+max+turn+signal+relay+location

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I'd at least invest some time and remove the head and look to see what you are working with. Have the head dye tested and also checked for warpage. if the head is OK, then do the gasket. If you severely overheated it, or if you had other engine problems before the head gasket failed, then I'd get a replacement engine ( many choices available from local craigslist, scrapyards and rebuilders ). Be sure to find the cause of the overheat that led to the gasket failure, otherwise you can do the same thing to the new one. If it's an automatic trans car, change the trans fluid also as it breaks down when it gets too hot.

may be a leaking fuel regulator or an issue with the coil pickup-is it a sputtering type of stall (fuel), or a dead miss (electrical)?

Have you tried adjusting the idle speed at the throttle body?

sounds like timing or a spent cam.

you can get pressure specs from your local parts dept, and check injector signal with a noid light

Throttle position sensor, check this out. Also try cleaning the throttle body with throttle body cleaner may be all it needs'

try this. disconnect battery.30sec reconnect. Hold engine at idle until it idles by itself. leave idling 20min.Computer can "forget" how to idle engine if battery has been replaced or disconnected.Dunno about check engine light.May disappear after bat/dis. Otherwise check wiringconnections around engine.

A lot.
Fuel cut off valve
Wire harness
Pump.
Etc..