Did you swap the bulbs? Are the flashers tied together or controlled separately? If tied together, test continuity between the working and non working. If separate, trace it back to the board. Test continuity at the board. Perhaps swap wires at the board so the transistor that's controlling the working left controls the right. If the rights come on then then it's a board problem. Otherwise it's wiring.

"Continuity seems alright" means what exactly? How did you test it? You tested the left wire on one working socket to the left wire on the non-working socket and the same with the right and it was continuous each time? If that is true, then perhaps the socket, itself, is the problem.

Nice work! What was the connector issue? Were there just a couple of connectors plugged into the wrong spot?