Phak1 wins the prize for suggesting the cause to my problem.
Started at the connector wires by the master cylinder with my new voltage tester. There is a purple wire, white wire, black wire coming from vehicle harness. With left turn signal turned on, I had a good flash on the voltage tester on the white wire. With right turn signal on, had a good flash on purple wire. Black wire had steady light on tester with headlights on.
Twisted the three wires to the leads going back to the tail lights. Connected white wire to the wire going to left rear light for brake/turn signal. Connected purple wire to my wire going to right rear light for brake/turn signal. Connected black wire to the wires going to each rear light for the tail lights.
With rear lights back in the circuit, I checked the voltage at each contact within the left rear light. Had good flash with left turn signal on at one contact, other contact indicated voltage with headlights on. I then inserted the bulb back in socket and tried the left turn signal, same issue with poor flash and both sides flashing on wrong filament. I then connected an alligator clip jumper wire from left light housing to good ground and the left light WORKED FINE.
Thanks to all, especially bartamos for the help and detailed steps to take for diagnosing the problem. Now, I need some more detail on how the left turn signal and tail light circuits, which really should not be connected, get crossed when the light housing doesn't have a good ground? Is it happening within the light bulb somehow?