Reverse light fuse keeps blowing ... anyone know of a likely cause please?

It might cost you a couple fuses, but pull both bulbs, put it in R and if it blows without a bulb, you've got a short somewhere between the shifter and the lights. If it doesn't blow, put in 1 bulb only (L or R) and try again. Then pull that bulb, insert the opposite side and put it in R yet again. That should help you isolate if there's a short in one side of the wiring or the other.

Of course, if you have access to a VOM, you wouldn't have to risk but 1 fuse.