According to friends that have owned them, LHD/RHD swap is mostly flipping parts over.
On RHD/LHD wipers on my era Jag, the motor needs to have the field reversed, and the park switch in the motor reversed, since when you shut the wipers off the motor runs backwards, there is an offset drag part that changes the sweep, and it parks against the windscreen trim.
I don't know if Minis did the revering and park bit. You'd know if when shutting them off, most of the time it does a second sweep and comes down further...plus RHD jags park on the rights (different arm bends), LHD parks on the left.
I have a motor here that was in the Jag when I got it. Single speed, which is wrong, park switch removed..I think it was a Morris, if I recall the numbering. Maybe the gear is what you need. Have a part number on the gear you want? I'll check later.
Dave