The best way to check out this sort of problem is to allow current to flow SAFELY so that you don't burn up wiring. What you need is a current limiter IN SERIES with battery ground
One good way to do this is to use a headlight, or an old stop/ tail lamp
You can wire both wires of a stop/ tail lamp socket together. So hook the shell of the lamp socket to body ground, and the two socket pigtail wires together, and hook them to the disconnected battery NEG post.
Now the lamp will light if a load is turned on. Remove the dome, trunk lamps and fuses one at a time if necessary to get the lamp to go out with the key OFF
Now, think to yourself "do you know for sure?" when the switched smoked?
Did it smoke in "run?" Are you sure?
Only in "start?" Are you sure?
If you think it was only in "crank" first try disconnecting the yellow wire at the start relay. Twist the key to start and see what the lamp does. If it's dim or out, you have found the area of the problem. IF not the problem is back from the yellow, through the bulkhead connector, towards the switch itself.
If it turns out that the "run" circuit is the culprit, start disconnection components one at a time. Disconnect the alternator field, unplug the regulator. Unhook the ballast connectors and unplug the ignition. etc