After opening it up, and pricing a replacement, I decided to make a new one. I chose to use the venerable 555 driving two small transistors in parallel to switch the lights.
I made the PCB to solder directly on the base of the failed flasher unit, which I de-soldered from the original PCB. Sometimes the first time is the charm - it worked when installed.
It makes no noise (the clicking was the relay in the original flasher) and it was a little strange at first. Of course, the really odd thing is that LR put the turn signal lever on the left of the steering column - on a right hand drive vehicle!