Those gears are different than what I saw at the shop. There was no space between where the angle of the teeth changed. I don't think they were capable of being engaged and disengaged. They were probably intended to be installed on 2 parallel shafts, which would effectively change the direction of rotation from input to output shafts. The only I can see that they could be engaged and disengaged is that if the shafts moved away from one another. Shafts in gearboxes generally don't do that because they need to be firmly located due to the stresses placed upon them. It's gears that generally move in a gearbox, not shafts.
When my partner and I first got together, he worked for Arbiser Machine, making gears.
And yes, both my Fieros gearboxes whine. In all gears.