It does sound like a bad ground. Assuming, again, like the older trucks(Ford kept the same style of wiring for close to three decades), there are grounds at the headlights, rear tail lights, steering column. The headlight/dimmer controls headlights, marker lights, dash lights. My guess is if you break out a wiring diagram you find that the ignition and this circuit share a ground at some point. Otherwise, a hot wire(not likely) BUT it could be in the key switch, VR or starter relay if still the old school types. Looking over a diagram will help narrow it down. Could also be fuel related since FI but normally on the old Fords it is grounds.
Try this, assuming it still has the floor activated high beam...unplug it and try it then. Very quick test.
To put some perspective on how funky grounds and these systems can be, on my '75 F250 4x4, I restored the entire column. Wire correct, had my rear light harness removed....turn on the the lights and one blinker indicator would like up solid, hit turn signal stuff went silly. Made 0 sense. After checking, rechecking, and more checking, I started playing. Can't recall the fix, but it was nothing to do with my wiring/restoration.....just how the system feeds, directs, grounds and it was one of two switches/several grounds/stuff not even hooked up. I did not take the time to look further since it was easy for me to get back to 100% being in the shop and tore apart.
