Gee, irregardless of whether or not the switch was wired hot or not, if you turn on the switch, be it a throw or push button type, the lights will come on, and the covers, if installed will melt.
I agree, if wired to ign Hot versus B+, the ignition switch would cut them off.
So, not sure what you are trying to say, except you accidentally hit a switch and burned your covers. Hell, I have done that a few times myself with aftermarket lights. From experience, the covers will not burn, but will melt quite nicely.
My experience comes from a lot higher output bulbs than the 55 watters used on the factory lights, I never started a fire.
Also, hate to inform you, this is not considered an "electronic" circuit, it is an electrical circuit, we are not talking in milliamperes, but in AMPS. There is a big difference between the two.
Want to change it to a ignition circuit, write me and I'll send you the exterior light schematics. With your experience, it should not be a problem.