on my 72 duster, I had an almost identical turn signal issue after I converted to a 69 valiant grill. key on ...engine off it gave me slightly different symptoms than when it was key on ....engine running (so I figured whatever it was had to be getting slightly different with the added current draw and or output during run conditions).
I went through it all, I tried replacing bulbs,removing bulbs....etc...etc..,check wiring, fiddling with the turn signal arm,messing with the headlight switch and wires, checking fuses and relays,replaced the blinker relay......still was having issues with it. What finally ended up fixing the issue ended up being.....
(cant remember off hand if the dusters factory turn signal housings were like this also or if other a bodies are aswell) but on the 69 valiant grill, in the turn signal housing there is a built in male electrical connector tab. so on each housing I made up a ground wire with a female connector on one end and an eyelet on the other end. Plugged the ground wire into each signal housing and grounded them to my core support. That did the trick, no more funky signal issues and that got the dash lights working properly aswell.
for whatever reason the factory signal harness's worked correctly with my factory duster grill but not ater converting to the 69 valiant grill. my best guess would be to try and run some quick separate ground jumper wires at each signal socket and see what that does for you....if it cures the problem (which I am inclined to think it will) then you can work up a permanent ground wire fix from that point.
hope that helps.
