ignition switch

Time to do some real troubleshooting. Download a shop manual:

http://www.forabodiesonly.com/mopar/showthread.php?p=1970088617

You could have a bad connection in the ignition switch connector, or the bulkhead connector, or in the circuit (ammeter) feeding the ignition switch

Clip your meter to the coil + terminal and ground, and crank the engine using the key, see what the reading is during cranking.

Turn key to "run" with engine off. Read both sides of ballast to ground. One will be higher, that is what you want. Leave that meter connection, move the ground lead from ground to battery POSitive, which will give you a very low reading. The higher, the worse the voltage drop. If more than .3V or so, you are starting to have a problem. If more that that, you have a "real" problem.

Recheck the above setup with headlights off, headlights on, and see if it changes dramatically