need help with transmission

I am guessing you see the lever on the cross shaft moving as you move the reverser lever forward and backward. I had one that the lever clamp bolt had come loose and the shaft was pivoting in the lever I think. You had to hold the lever hard to the left to get it to shift forward or backward. If you are seeing the lever moving with the shaft, and your reverser lever has minimal side to side movement, I expect you have a broken shift fork.

In any case you would access the mechanism by draining the oil and then disconnecting the interlock linkage and removing the cover on the left side of the transmission. This removes the complete interlock mechanism. Then you can remove the complete shifter fork group by taking out 4 large bolts that hold the two vertical supports. The assembly rotates outward at the top and comes right off. Then you will have access to the lever that is mounted on the reverser shaft as well as the shift fork itself. The forward/reverse fork runs on the bottom rail and is the front most fork at the bottom.

I have those parts in a disassembled transmission if you need them.

The reverse idler is the one Ray is talking about I think.

I believe it must be ok since the tractor goes in reverse just fine.