HELP!!! Electrical Gremlins in an '84 K30

[LMN8R87]

I've got an '84 K30 crewcab dually. I have no rear (past cab) running lights at all. The side (on rear fenders) clearance lights come on with the brakes. With the signals on, both main taillight bulbs flash, until the brakes are applied, when the main bulb stays lit, but then only the secondary bulbs flash. All lights forward of the bed work as they are supposed to.
My second issue is that if I drive the truck for 1/2 hour or more, shut it off, then try to restart it, it acts like the battery is dead. No clicking, no dragging starter, nothing. If I jump it, it starts right up like nothing ever happened. Are these 2 issues connected, possibly? Any Ideas on where to start digging? It appears that the factory wiring is still intact, fortunately, so it isn't a previous owner's hackjob. Any help is greatly appreciated!
Thanks to all,
Rod

[donut]

I'm by far an electrical wiz, but first thing I did with mine was clean all of the grounds. thus eliminating them as a problem. I also cleaned up all of the sockets, one at a time. Road salt and time can do a number on them (this was on my old plow truck)

On the C-30, I had no running lights and intermittent brake lights. Turned out to be 2 problems. Old trailer wiring had corroded and crossed everything up, and every running light bulb was blown. IIRC, I also checked the entire line, feeling for cuts, bulges etc. thinking maybe a pinched wire.

Same thing with the starter. check all of the connections. I believe I just replaced the battery cables as new ones were cheap enough, and cleaned the starter connections.
For piece of mind, I dropped the starter (easier to inspect/clean connections) and ran the starter to Auto Zone and got it tested.