I've only noticed the bouncing at night with the lights on and the engine at idle stopped in a left hand turn lane waiting for the signal light to change. The tach doesn't bounce with right turn signal on. And it only moves about 1/4 inch when it does move, but it doesn't move all the time.
Armed with more symptoms, as Al suggests, change the flasher for a 552, a heavy duty, I will suggest swapping all three bulbs side-for-side and ensuring the correct bulbs are used, meaning the same part number and see if the problem follows the bulbs.
All of them the same type within the bulb number, ie, 1157 for both swapped, not one of them being a 1157LW and the other a 2057 or a 1157LL. Make all of them are the same part number regardless of bulb used.
If problem does not follow, then look at socket grounds at both ends/corners of the lights.
If the above suggestions fail, and right side signals have no effect as left side signals, then temporarily jumper tach power to the BAT spade on fuse panel or battery itself and compare results.
Since it only does it with left signal and not right I would start by checking the ground on the tail light house itself. One test is run a ground jumper from the housing to a bare metal part of the chassis and see if the symptom goes away.
GMPP ZZ383.... running an HEI distributor I would assume. Might also want to check the 12v power source and that you have the right gauge wire feeding the distributor and also the TACH feed wire on the HEI. HEI's can do weird things when they don't get a very solid 12+ volts.
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