I think you have a bad ground on one of your parking/signal lamp housings. I'd start with the right one and provide a temporary alligator clip ground if possible.
Reason I say that, if you look at this schematic:
http://www.mymopar.com/downloads/1969/69ChargerB.JPGNotice that the directional/parking lamp bulb (under the 2 headlights) has a common ground for the directional filament AND the parking filament. If you lost the housing ground then the parking filament voltage will flow thru the directional filament and make its way to the directional indicator bulb in the dash (which one side is grounded) and it will glow dim because current is reduced due to the directional filament and the dash indicator filament resistances.
You can apply a GOOD temporary ground to the housings OR take an ohm meter and read from the housing to the frame etc. or better yet to the negative battery terminal. Should be close to zero ohms, certainly under 5 ohms.
Please let us know what you find.