62 Rambler Classic no reverse or park

Read the section on the shifter and on operation of the trans. In the 62 TSM that's pages 7 & 8 of the SHIFTING SYSTEM section (last tow pages) and pages 5 & 6 of the FLASH-O-MATIC TRANSMISSON - 10 SERIES section. Page 22 shows how the linkage inside the trans works (is removed) -- that might help. Shifter and park cable adjustments are on page 42 of the trans section. There is a diagnosis guide on page 63 that might point you in the right direction. The V-8 (Series 80) trans is pretty much the same internally, though the housing is heavier and the valve body slightly different. The Series 10 section is better illustrated, so look at it even if you have a V-8.

That's probably correct... but might not be. Check the main case (just above oil pan) with a magnet. If it's an aluminum case it's a M-35 (called a T-35 early on, the M designation didn't come along until later models - M for model, T for Type -- changed to prevent confusion with BW manual trannys). If it has an iron case it's an M-8. The TSM doesn't list the model number for either since the 35 was only used behind sixes and the 8 behind V-8s.  Since the trannys look very different in the TSM I'm assuming you do have the 35. That was the first year of the 35, that's why I mention it could be the older M-8 -- all engines used the M-8 from 57-61. It's possible that an early 62 model had the older trans, or it was swapped out at some point in time -- the car is 59 years old!!