Strange electrical issues with my '72 Dodge truck

As RedFish mentioned, it might be related to your ignition switch swap and a cross-wiring issue. What brand ignition switch did you use? Another possible cause might be improper, missing, or corroded ground(s). In the start position, that has the biggest current draw of any stock system. If you don't have sufficient grounding, the current will try to find another way to ground, sometimes that being another circuit or even hard lines and/or braided cables.