[VetteVet]

I would suspect the connections in the turn signal switch or possibly the two dash turn indicator lights are shorted together. I don't think there is anything wrong with the flasher.

Here's how to troubleshoot.
to eliminate the turn signal switch, disconnect the half moon connector under the dash and locate the half that goes to the front lights.

find the purple wire in the center of the connector, this is the power wire for all the turn lights.
With the key on this wire has 12 volts power on it from the flasher to light all the turning bulbs.
Jump this wire to the dark blue and the dark green wire in the same connector, these are the right turn light wires, and see if the left turns also flash.

If only the right turns work then there must be a short in the turn signal switch.
If the problem persists then pull the cluster plug connection to isolate the turn indicator light wires in the dash and try the test again. Post back with the results.