Ford 4-Speed Toploader

I have a 1972 Ford Mustang, 351C-4V, 4-speed toploader, Hurst shifter.
The speedometer does not work (at all) so I replaced the speedometer
cable and reused the cable driven gear inserted into the extension
housing. Still doesn't work. I can feel the output shaft in the
extension housing with my finger through the speedo-gear hole. I can't
feel the drive gear on the output shaft. Is it possible that it broke
off and is in the bottom of the extension housing? Could such a gear
(plastic) just break off? If so, what's the best way to replace it
now? Does the whole transmission have to be removed or is it possible
to somehow remove the extension housing to expose the output shaft?