...the guy I bought it from said the gears were "backcut". Not sure what that means or if it could have anything to do with the sound.
I'm going to take a guess from way over here, no trailer needed.
This was back in the day you would tumble the gears so they'd be nice and polished in walnuts was it? The other trick was to 'backcut,' meaning, the 'dogs' or the nipples that stick out of the gear, the dogs enter the slots in the other gear.
While this dog is pushing the other gear in the slot, we want a lot of meat there, because that is full surface dog side on that one side of the 'dog tooth' is being slammed into that slot, so you want the most bite, the most contact. That's the load side.
When you lift, roll off the throttle, the dog is now being loaded on the coast side of the dog. Under Load it's quiet, right? Coast it whines as in take a wet finger and rub it around an empty wine glass. Hear that ringing right at the edge of the glass? How much surface is touching that lip? Not much, right?
This is now the sound of the coast side being the 'back' side; is having less material [contact] at the back of the dog; so it sings/rings; is the 'cut' side; is the noise you hear on lift. Why the cut? At the time, we had toggle switches that dialed in rev limiters to the coils, but could not think of setting up a kill switch to the coils at the time. So the backcut was trying to out shift the lift that happened in that short a slot. Old style goes; lift off the throttle, pull the clutch in, all that time and coast was there in a millisecond. So it was easier to pull the gear out under that instant coast load with less material to drag out of the slot. This way you could pop out easier and shift more solidly to the next gear.
This turned that gear trick for racing obsolete. They now use a built-in shifter that kills the spark. Now, no engine load under lift; no clutch lever pull; no throttle lift; just shift with the hand at WOT.
How close am I? U-haul and I haul a theory.