Transmission Identification - Hellllp

I need to drive my 2+2 (I6 with 3spd manual) temporarily before doing the V8 swap. Problem, the syncros in the 2+2 3 spd are shot so I bought a 3spd transmission from an I6 - 64 Falcon thinking it would swap right in. Nope . Got it home and it looks basically the same but the shaft length on the Falcon 3spd is shorter. Also there are no shift linkage bolt connections at the rear end of the Falcon trans but the Mustang 3spd has them????? Gear cluster inside is the same though on both.

So what trans is in this Mustang (it may not be original)? Ford's Dagenham 3 spd has 3 linkage connectors on the trans (1 for reverse) but mine only has 2. Both the Falcon trans I bought and the Mustang trans from the car have top inspection plates, 2 linkage connections and the same gear cluster inside the box. I took the Falcon trans apart to get the good syncros out of it and am going to take it to a shop to have them installed on the Mustang 3 spd.

What the hell? How many I6 3spd transmissions did Ford have back then? I'm not sure what I have in my Mustang.

Can anyone help?