My tranny did the same thing but it was 1st and 3rd. This is what I found. My tranny is a W56B I am not sure what model yours is but I am sure it is similar inside.
Here is a picture of my mainshaft and gears.
The bearing at the bottom of the picture I call it the center housing bearing was worn out causing the whole shaft to move inside the tranny when you put it in first or third gear. As you move the shifter forward inside the tranny it moves the shift collars back over the brass syncro on to the gear. If the bearing is worn out the shaft moves further than the throw of the shift collar ( thats why its fine if you leave your hand on the shifter) witch does not fully engage the holding keys of the shift collar.
Hears a some pictures of my worn out bearing
In this picture I am moving the inner race with my finger to show the play it had. It should not have moved at all.
This one shows the wear itself on the races. They should be smooth not pitted.
Oh welcome to the board
Scott