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If it is the light duty 3-speed of old then the low gear is unsynchronized and slides on the main shaft only when shifted. It either goes into the reverse selection or it goes into 1st gear. If the low/reverse gear is moving around, cluster gear is moving around, or the main shaft is moving around too much, there could be a problem. The clutch definitely has to be doing its job when releasing too as was mentioned. The shift tower may also need inspection of the tip of the shift lever and the slots it fits into. Make sure there is plenty of lube in the case. That's what allows the cluster gear & main shaft to slow down when you depress the clutch control pedal.
There can also be a problem with the pilot bearing. If it doesn't allow the input shaft to move free of the flywheel with the clutch released, you will have a problem.