Parking lights and side marker lights stay on constantly

[dmjlambert]

You didn't say what year your truck is, but if you're talking about something earlier than 1973, there is no connection between key switch and tail lights and headlights. I see in other posts you have a 1966 truck, but I don't know if that's the one you're working on for this electrical problem.

You likely have some customized wiring in your truck, because in a stock truck the key switch has nothing at all to do with headlights or marker/tail lights. Show us a wiring diagram for your truck and somebody could probably give clues about what to look for next. Or you'll have to inspect the wiring and trace the wires and see what devices they go to. My guess is you added a relay (or hired somebody to customize or previous owner customized) to switch off the lighting with the key switch and perhaps have a daytime running light circuit (also something custom or more modern), and one of the relays is bad. It's also possible you have stock wiring but some of it is damaged, and wires are shorted together. On my truck rats ate part of the insulation off of several foot-long strips of wiring that were in the frame rails and inside the front fenders and under the battery, and I had to do some repairs.