I wanna say C6 but it's escaping my mind at the moment, I'll double check when I'm able. I believe it's original. I got it from my father so I'll just double check with him also but I'm banking on it being original, i haven't heard otherwise. The fluid looked okay last time I checked. It's been sitting this Summer so I will check it soon to see if it has changed or not. I don't think it's been changed in a long time. I had it in the shop recently but I don't think they changed or looked at it.
When I put it in every other gear, it doesn't always sit properly but it'll go into gear. Drive also acts funny sometimes but OD works the best. Reverse is just temperamental.
It may just be a linkage adjustment problem.
With it running and your foot on the brake, move the shifter slowly from park through all of the gears, pausing at each one for a couple seconds. (pull the lever towards yourself the whole time.) This should allow you to feel the detents in the transmission internal linkage. Make sure you pause at every "click" you feel. Reverse should be the first one.
If it engages at this point, a linkage adjustment will be required. If not, the problem is likely in the transmission.
If you still can't feel reverse at this point, take it for a drive (IF its drivable) and do the following.(If its a C-6)
Put it in man 1 (All the way to the right) Accelerate to 20 or so and lift your foot off of the gas. See if the engine seems to slow you down (Engine braking), Then drive and see if it has 3rd speed.
A C-6 uses 2 clutches, the direct, which is used in 3rd, and low-reverse, which provides engine braking in manual 1st. If either of these functions are missing, it will indicate which clutch has the failure.
Note: an AOD has different band\clutch applications, so this wont work there. We will tackle that one if we need to.
Hope that helps.
Cheers