NEED HELP ASAP on ignition

You need to chase down where that brown goes. It should not get hot

What kind of ignition?

Mopar ecu with 2 pin ballast?

Mopar ecu with 4 pin ballast?

Other aftermarket?

Does the wiring look hacked/ repaired?

Below is a simplified diagram. If you have a 2 pin ballast, ignore the top left terminal which isn't there, and imagine the bottom left terminal is part of the bottom right terminal

The colors in this diagram may not match yours

The "dashed brown" should. As you can see it only goes from the switch, to the coil+ side of the ballast. You should be able to trace that pretty easily

NOTE something I didn't think about is your coil may be bad/ shorted. You have another coil you can try?

Notice that they call these out as "ignition 1" (run) and "ignition 2" (bypass) which is what Mopar calls them.

(Thanks to whoever originally posted this diagram, it's pretty good)