is the whole tower wiggling about? there is a bearing in the base of the gearbox for this, its the one with the VW logo on it with a bolt either side. there is also a 'ball sleeve' inside the shifter tower that can be replaced. you really need to check the thing over carefully then tell us where the play is coming from, as it could be a number of things.
as for gear linkage adjustment, try this:
The mk.3 16v has the same type of gearbox as the VR6 (and Tdi for that matter), the '02A'. You can check the transmission by selecting at the so-called 'tower' mechanism on the gearbox. Look for the balance weight on it, which looks like the head of a golf club. It has the two cables from the gearlever inside the cabin attached. The lateral cable adjustment might have slipped. When this happens, then basically the gear lever and gearbox selector are out of phase, and selection problems occur.
selecting gears at the transmission
Get hold of the weight and use it to push the selector mechanism right down, which is meant to correspond with the lever being at the left side of the 'gate'. Then move the weight (and the lever it's bolted to) CCW, towards the engine block, to select reverse gear. If the ignition is On, the reverse lamps should light when you find reverse. If it's not possible to get reverse, check for damage to the plastic/metal 'U' bracket which lifts and lowers the selector mechanism, or the adjustment nut being loose in its slot. If necessary, carefully detach the lateral cable by lifting the retaining clip and slipping the cable end off its peg. Then try selecting again. If you can now get reverse, the selector adjustment is at fault, but if not, check that the selector mechanism is firmly attached to the transmission. If it is, suspect the transmission.
Selecting 5th gear is similar, but lift the selector to its upper limit and then turn ccw.
home adjustment method
The gear selector mechanism is sprung to return to the mid-point between 3rd and 4th, so the main thing is to attach the cables to the gearbox selector with the gear lever at the same point. Moving the gear lever forward/back moves the lower cable (at the gearbox) to turn the selector lever, with the weight, cw/ccw. Moving the gear lever across the gate lifts the selector mechanism up/down using the upper cable and a relay lever - watch as someone moves the lever from side to side. Adjustment of this cable is done by moving the flanged nut along the slot in the relay plate. There is a special jig used by garages to hold the gear lever while adjusting the cables, but it is possible to get the adjustment right wihout this by trial & error; the plastic part of the relay lever seems to have quite a 'flex' in it, which has to be allowed for.
The lower cable is adjusted, if necessary, by loosening its attachment bolt and sliding the head of the cable along the edge of the selector lever; a caged nut inside a track on the lever moves while the bolt is loose. Adjustment is ok when the gear lever can be moved across the gate with the transmission in neutral, without having to move it forward or back.
But since you mention 3rd/4th selection is alright, with luck you'll only need to repair/adjust the relay lever. With the upper cable detached from the gearbox, and after replacing any broken relay lever parts, place the adjustment nut half-way along the slot. Put the transmission into either 3rd (ccw) or 4th (cw) and select the same gear on the gearlever. Then carefully re-attach the upper cable to its locating peg, so that the gear lever and selector are fully connected again. Move the gear lever out of the selected gear; it shouldn't move sideways, but remain lined up on 3rd/4th. Any sdieways movement can be corrected by slightly loosening the adjustment nut and moving it along the slot, allowing for the tension in the linkage. The direction of adjustment depends on which way the gear lever requires alignment. F'rinstance, if the gearlever lies too far to the left, move the nut slightly to the left in the slot.
