That is a bit of a strange one, if staying in gear and doing it
I'd also check all the engine and transaxle mountings for excessive compliance, levering them around to see what is moving that much when reversing?
As Aidan says, get hold of the main selector shafts adjacent to each bush and see if theres lots of radial play in the bushes. Or get someone to go through the motions in the cab and watch the selector shaft, partic. as they slot it into G or R gears. They shouldn't be snatching up and down or side-to-side, just sliding through the bushes.
If there isn't excessive play in the shaft bushes, or the gearlever pivot bearing, and it's staying in gear, yet the lever's jumping about when reversing,
it's probably unhooking off of the 'G' & 'R' detent stop, under the cab, possibly due to maladjustment (at the centre spline join, just behind the main cross-member) - the whole system is not something to easily talk through setting up - it's a bit of a black art, but read on, partic. the Wiki. Bentley manual also gives some setup tips and clearances that worked for me, or at least get you within the right ball-park when re-assembling from a complete strip-down.
Check the Wiki out, which describes the whole system in some depth, become well acuainted with what to expect before diving underneath...
Sloppy g/c and description of selection mechanisms
and first though, check the front gearlever floor pivot for bad wear:-
Gear lever pivot repair