I have a 78 camaro type LT, came factory 305/350 auto floor shift, limited highway rear end, now custom with 318,000km. I've had this problem for almost a year now. I've re wired the car bumper to bumper aside from the original harness from the fuse box to the rear connection, the headlight switch and signal switch are also original. I've replaced every socket, the harness for the front lights and tail lights and grounded everything individually. My problem is that with the car on with no running lights and you turn the right hand turn signal on the indicator flashes as well as every light on the car except the front two amber lights, the headlights, left hand and both brake and back up lights flash with the indicator and when you turn the running lights on or headlights on it all stops flashing and the right hand indicator stays on steady all the time. However the left hand signals function 100% normal. I have bought a new turn signal switch and just plugged it in at the bottom of the column, it didn't change anything.
all the wiring under the dash is was original when this problem started.
I have replaced the front lighting harness from 4" in front of the fuse box, the fuse box, main connections and under dash wiring is all original.
anyone with any ideas would be greatly appreciated, budget isn't small I'm just on no hurry to replace all of it yet aside from being 39 years old it's still in pretty good condition and I'd like to have her running properly for summer.
thanks for reading,
Rob.

 

I have seen similar symptoms twice before in second gens. Both times it was a damaged wiring harness. In both cases a patch panel was welded in the drivers rear quarter and that cause the harness to melt together.

The turns signal switch can cause the same issue.

 

Thank you for your reply and sorry it took so long to have an update.
I completely rewired all the front Amber lights and just temporarily spliced them into the wires going to the rear of the car. After that when the right turn signal was on the right rear Amber was flashing but the front left Amber lights alternated flashing and still nothing from the front right. And everything still works fine on the left hand signals.
beginning to think it could be a short in one of the left side sockets

 

Update.
I cut the running light power wire and grounded both front side markers and it works now.
still haven't found the cause of the problem and now I have no front running lights.
leaning towards a short in the headlight switch or running light power line​​​​​​

 

Solved it, I almost feel dumb for not figuring this one out sooner, turned out to be the connection from the harness into the dash printed circuit.
the printed circuit had dried out over the years resulting in crossed connections.
I pulled the dash, flattened and lightly glued the copper strands in place as none had broken. I haven't tried my running lights I'm hoping this solves it