I'da guessed with Rach, but if you're certain you can exclude that...
Non-HO Zonger base? Does it also, when pushed in neutral, leaned one way or the other, try to grab a gear some times?
Yep, check both ends of the shift drum next. I'm gonna venture they're both snug.
Next, while both ends are available, put it in neutral and push the drum back and forth. More than a tiny bit of end play and it's the probable culprit. You can modify a washer for the left end to have a recess to slide over the end of the shift drum stub, source a thin shim to go around the stub and be held in by the regular washer, or correctly,,, split the cases and remove material from the end of the stub to give minimum end play. While in there, make sure the gear dogs and slots that have been skipping apart aren't too badly damaged. Gears are cheap enough. Shim the ends of the shafts if needed, to give minimum end play. Staggering shims to increase the engagement on the 2nd gear helps.
