Try this to isolate the affected circuit. Start pulling fuses one by one for the lights involved. Put the fuse back you just pulled before pulling the next one. Hopefully that will give you a glue.
Also since you are in PA where rust is a "thing" a frame harness may have been compromised.
That generation Ford had corrosion issues at the top left corner of the windshield allowing leakage down onto the components behind the dash on that left side. That's where the headlight switch is. Ohm your switch or try a new one. Maybe you have a pal that would let you try his switch. You don't have to pull yours, just pull the connector down to plug into the test unit.
Do the 4 ways work correctly? Do you have a trailer connecter in the bed?
Something is back feeding either due to a bad or missing ground or a bad switch somewhere but the delay puzzles me. I hate these type of problems and a lot of techs just throw parts at them and hope they get lucky.
Puma 30RKSS