I had ALL of those mentioned problems right after I took the main dash out and replaced the vinyl. Once I reset ALL the screws to the dash, ensuring each screw was locking in to its intended target, the electric problems went away, like....immediately! There are a few dashboard screws that do infact ground several systems, though you'll never see that on a schematics diagram. Check all those dash screws, make sure they are linking up with the nutplates. Pardon the language, but make sure every hole has a screw in it, the right screw!
'68 428 HO M3 Monster, 4-on-the-floor! Need I say more?