The reason we ground the circuit at the lights is to control where the circuit completes. If it does not ground there it will find a way to do it by going back thru another wire if it has to.
By that reasoning, I should probably look elsewhere from the actual lighting circuit for the 12v source.
Here is my thought. If I can get only the dash and arrow head lights to turn on via the rheostat portion of the light switch, with it in the off position (all the way in), power must be feeding from elsewhere. (Unless the rheostat also controls the interior courtesy lights when the light switch is in the off position, I can't remember if it does.)
Does this possible scenario make sense... My ammeter used to work. It does not now. It has a light in it. Power is fed to it via the printed circuit board. If it is bad, it might feed back through the light into the rheostat and cause the arrowhead light issue. Additionally, when the lights are in the on position, power may feed back into the ignition system since the ammeter is part of that system anyway.
Maybe?
68' Firebird 400 convertible, numbers matching, solar red w/ deluxe parchment interior. 66' Pontiac Ventura Hardtop 66' Pontiac Catalina Convertible