As mentioned flasher may be bad. They're cheap, truck is old, easy to replace, maybe time anyway.
But that doesn't account for no running lights or reverse lights.
Bad ground? Maybe but you said all lights grounded individually.
Wiring melted? Distinct possibility.
I'd start with the trailer plug in and work my way upstream. I think the early Powerstrokes were plug n play on the trailer plug from the main wiring harness to the tail lights. can you unplug that and eliminate it from the circuit?
Maybe take trailer plug apart and see if anything is loose, unhooked/touching another wire.
Good luck.
My last electrical fiasco was on my 86 GMC last year. Clean truck, pretty clean wiring, incorrect/intermittent dome/courtesy/cargo lights in cab. After spending far too much time on it, like 2 whole afternoons and coming up dry on any wiring issues, I discovered someone before me put the wrong style bulb in the cargo light!
