My first car was a 62 Comet. Then I had a 65 Falcon 4 door and a 65 Fairlane 4 door much later on. These are all the same car basically, including the mustang. The other fords are different, like the galaxie. I used a lot of junkyard parts from the other cars that were the same. None of the junkyards had a good 3 speed manual transmission for the 6, so I actually rebuilt the one I had, using parts from a mustang transmission. That was the little 3 speed, first gear wasn't syncromesh, meaning you couldn't downshift intio first, you had to come to a complete stop. That's why it was easy to rebuild, not a ton of parts. Only the 6 cylinder engines got that transmission. Yours looks just like the one I rebuilt.
Ask me if you have any questions on the falcon. As a teenager, I broke and fixed everything on that car. I still have the big Chilton's manual 64-71 here somewhere.