The obvious first suggestion is to check that the gear lever isn't fouling on anything, like the footrest mount, which could be stopping it going right into gear. After that, all I can think of which doesn't involve stripping it down completely is the detent behind the large primary gear. Behind the gear is an arm with a pivot in the middle. At one end of the arm is a spring attached to a peg in the crankcase and at the other end is a wheel. The wheel bears against the end of the selector drum, which sticks out of the crankcase. On the end of the drum is a star shaped cam washer, with a normal washer on top of it, all secured with a countersunk screw, and it's the cam washer which the wheel on the end of the arm bears against. I've heard of people having problems with the spring breaking or falling off, and in my current engine I couldn't get the countersunk screw to stay tight, so it would be OK for a few hundred miles, until the screw (and obviously the cam) worked loose and the gearchange became a bit "woolly". A drop of superglue on the thread a couple of thousand miles ago seems to have cured that.
Failing that, I think you're probably going to have to take the engine out and split the crankcases.
My first ETZ used to jump out of third gear whenever you opened the throttle. It turned out the selector fork was badly worn, and wasn't pushing the sliding gear
quite far enough to engage the dogs properly. The MZ gearbox relies on slight undercutting of the dogs so that they pull each other together once engaged, so unfortunately once the dogs had been rounded off the two gears were useless as well!
It's a pretty standard problem with 3rd gear in the five speed motors, but I suspect your problem is probably similar, so I'd be looking at the condition of the dogs on the gears and particularly at the condition of the selector forks. The wear the worst on the curved area where they sit in the groove on the gear, and you may well find they've gone a nice blue colour if there's a problem. The other ends of the forks have little pegs which sit in slots cut in the selector drum, and it's also worth checking both the fork and the drum for wear here, although they will probably be OK.
Good luck! At least the bits are all readily available. I had a problem with a worn fork in the Burman box on my Panther a few months ago. Couldn't find a new one, and the best old one I had in the shed really looked just as bad! I reckon there was a fraction of a millimetre in it though, because it seems to be alright - for now!