i don’t have any experience on this so my thoughts are worth about what you are paying for them
2 possibilities are something shorting 12v and dropping voltage to ignition when moving the turn signal
Or
Something moving cables/wires and causing some intermittent open in power to ignition.
Since key is on dash it seems unlikely to be the later.
You may be able to prove this by watching voltmeter on 12v at coil when lever is moved, not sure.
If it is something shorting, I don’t think there is anything to do but disassembling and searching
Hopefully someone has better experience and knowledge. Good luck