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