From your post wording could the broken arm be off from the side of the transmission directly behind or in front of of the control rod that is still connected to the transmission? Sounds like the arm somehow got broken off the transmission stub shaft that controls one of forks . Seen these broke/bent/missing when looking at used transmissions - getting broke probably came from transmission being rough handled at some point. My guess would be finding any 3 speed transmission of the same model at a salvage yard and compare - doesn't need to be a GMC - try a Chevy car/pickup.
