69 valiant electrical gremlin turn signal and license plate light

What I have done, and maybe is the best direction right now, is check that all the bulbs are good (both filiments) and properly seated in their sockets.
Also check all of the connections, especially the grounds.

After that is all done. Then do a systematic functional check.
Turn on the parking lights. Walk around and see if they are all the same brightness.
Turn them off.
Turn on the right turn signal. Walk around and see what each lamp is doing, how bright.
Turn on the left turn signal. Walk around and see what each lamp is doing, how bright.
Turn them off. Turn on the Hazzards. Walk around and see what each lamp is doing, how bright.

Now you have a pretty good list of what is working and what is not.
Turn the parking lights on and recheck the turn signals and hazzard.

If anything is amiss, with the complete list should be able to narrow it down.
Put the battery on a slow charger since all that testing is draining the battery. Charging it on the charger will save other potential headaches later...

Here's the front end lighting diagram from the 1969 Dodge Dart-Coronet Charger Service Manual.

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You say your car is without the fender mounted indicators. So just erase those.
You can download the manual as a pdf from MyMopar - Mopar Forums & Information - Service Manuals