Transmission will not shift into reverse

A somewhat common problem is a broken low / reverse band. I've been involved with three of these since the late '70s. The best clue you can look for is to shift into "1", or "first", then drive a little ways. If the band is okay, the transmission will stay on low gear, regardless of how fast you go. If the band is broken, the transmission will up-shift to second gear at the appropriate speed, then stay in that gear until you slow down.

This first drawing shows the servos. The red arrow is pointing to the lever that applies the low / reverse band. The blue arrow in the second drawing shows the band. The arrow is pointing to the spot where they typically break.

Unfortunately, the transmission has to be removed and disassembled to do this repair.