Nobody will probably be able to give you a direct answer. Not the answer you want, trust me I know. You will get lots of ideas about where to start, but your going to have to put the work in.
From experience......and it started with my aftermarket gauges as well....... get your volt meter out, print out the electrical diagram, and start following your hot wires, turn signals, connectors from steering column to 8 or 11 pin connectors, turn signal cam/housing wires, to turn signal / hazard flasher relays, check grounds, check fuses, check lights, and then double check. . .
I just did my dash and it has been a domino effect of electrical gremlins. I've pulled my steering wheel off twice. I've found burnt wires from the past, bad grounds, horrible pin/connectors, bad light fixtures that don't make contact with light nipples, ....... and more.
I am doing it right now and once you get knee deep in that $hit you will know how to do it later. I am beyond frustrated with my wiring, but I now have the diagram printed, labeled, and can follow any wire path from hot wire to light, and back, and now know where my problems are. It is still not easy but I can do it.
I would start with finding where the turn signal and hazard relays both connect or can be influenced by one problem. They should be 2 different relays with 2 different jobs. Check your wire diagrams..... somebody will post a link for the 72 plymouth shop manual. Print the pages - dont be intimidated. It is like trying to get out of a maze with a pencil on the back of a cereal box. When you hit a dead end, follow a different wire, and repeat until you find were the problem makes sense.
My 2 cents - ditch the LED's - they made my life harder.
I know one day we will look at this car and forget all this frustration...... right?
