Taking the gearbox off is not the first thing to think of when you don't know if it is the gearbox or the saddle.
First run the lathe spindle only to make sure that and the motor are fine with the belts slack in case something does get stiff.
Then run the geartrain up to the box with both the gearbox handles dropped down so they are not in a setting detent hole just right down. They are then out of mesh. Run for a while.
Then engage only the left one, run for a while, then both, engaged.
Obviously without the saddle moving just running the gearbox (but make sure you have oiled it) and the belts slack.
If that is all fine the gearbox is checked out.
Put oil in the saddle gearbox with a small tray under for the drips. Move the saddle using the handwheel but apply varying amounts of longitudinal pressure to the saddle to see if that a affects it.
Finally try autofeed. If it has problems that is the apron not the gearbox.
I'll post later how to remove the bits.