84 Chevy else Camino distributor coil over heating

Check the timing.

Bad pick up coil in distributor or worn shaft. The wires on the pick up coil should have 500 ohms to 1500 ohms resistance.
Move the wires and vacuum advance while testing, reading should not change. Then test resistance from one coil pick up wire to distributor housing this should be infinity.
Wiggle the shaft and see if there is any sideways movement.

posible you have a bad ignition module or all efect switch in side the distributor

What do you mean the 1977 had no coil or distributor, was it removed or stolen?

Had an 84 silverado 305 that did the same thing. Try giving it a full tune up. Plugs, wires... Mine turned out to be fouled plugs. I didn't find that out till after i tore it down & put a timing set in it. Wasn't getting good enough spark.

Could be the coil, ignition module in the distributor, or various other things.
I would check the coil for battery voltage and resistance first.

MORE THAN LIKLY you burnt something like a fuse or a relay or possibily something in front or in back of the harness i know thats a lota help but different people have diff. solutions sometimes. CLOWNY DAGGERS

check or replace the bulb on the non working side

it could be the ecm"computer" that can cause know spark and know gas at the same time.