Running a gearbox backwards.

Could you run a stock gearbox in say an MX5, with an engine that spins the opposite direction?

Is there anything in the mechnicals of the gearbox that are designed to run one direction only?

With helical gears then their is a force along the shaft introduced which is countered by a thrust bearing. With it now needing to be on the other side of the shaft there may be problems.
There is also a different force as the gears usually mate off centre and this can affect the main shaft rotatinoal bearings but much smaller and less impact,

And of course now the car has 6 reverse gears and one forward :)

I was just calculating stuff on automatics today, but i think that these should be fine. The torque converter is the tricky bit with the vanes on the turbine- and pumpwheel pointing in one direction. If you turn these around I think the connected planetary sets should be fine.

A CVT is offcourse definately not a problem, except for the torque converter again. I guess if you do want to turn it all around the simplest solution is to add one extra set of cogs and just reverse the forward drive..

Put a 911 gear box in a 914, or vise versa. It's quite entertaining. Then you realize you have to swap the ring gear.

That was my first thought too, Johnny... like flipping a transaxle for FV use, too. But Kozy's MX5 example would be problematic as suggested by Matra. Helical gear mating surfaces and thrust points will be very different so I'm not sure it's wise to do it.
At the least it would be a very noisy 'box. Kozy, what engine swap are you thinking about?

Honda B series. IMO, perfectly suited to the dinky Mazda, just a shame that the engines spin the wrong way.