There is a good chance that some of the flasher relay contacts are not making good connection.
The flasher relay terminal layout should be terminals 1 thru 4, top to bottom, front of the box, toward front of car. Terminals 5 thru 8, top to bottom, rear of box, toward rear of car. These numbers should be embossed in the top of the relay cover.
Check: With the turn switch set for right turn, relay terminal 8 should read steady 12 volts to ground. The RT relay should be clicking. Terminal 1 should be intermittantly hot from the flasher can. Terminal 6 should be intermittantly hot to the RF lamp, terminal 7 intermittantly hot to RR.
With the turn switch set for left turn, relay terminal 8 should read steady 12 volts to ground. The LT relay should be clicking. Terminal 1 should be intermittantly hot from the flasher can. Terminal 2 should be intermittantly hot to the LF lamp, terminal 3 intermittantly hot to LR.
The cover can be gently pried up around it's edges & removed. The tiny relay contacts can be "very gently" cleaned. Even a rough piece of paper can be drawn between them. If you bend the delicate contacts even slightly, chances are good that the box will no longer work, so be very careful.
You may wish to remove & tag the wires & remove the box to work on it.
Good luck,
D