Yes, I see what you mean. Looking forward to what Derf has to say. From my investigations I've determined that the lever is part of the "Housing Kit. Transmission control lever (gm # 21005866)" which is no longer available. If the lever does not belong in the position shown in my pics, I'd be very curious as to how it got that way.

 

As parts start to wear everything gets a little loose until something slips into where it doesn’t belong.
See if you can slip the linkage back into the correct slot to verify that the transmission is still repairable and all the gears work.
I had a 65 Mustang in high school that had a lot of miles on it and the manual transmission would shift into 2nd and reverse at the same time. It only happened a couple times before I removed the transmission and had it repaired. A worn pin inside the internal interlocks let this happen. The output shaft instantly stops turning and you skid to a stop.

 

Sorry I will do pics tomorrow

 

The following pics are my best attempt at showing the linkage positions at the transmission connection for every gear. Upon further review, the neutral lever (which in previous pics was not in the correct position) was loose and I was able to get it into the proper "slot" as previously discussed. It would seem that the pivot point for this lever is worn causing it to move slightly up/down which enabled me to get it into the proper position. Also, it does not appear as though the pivot point would be a easy replacement unless, perhaps, it could be drilled out and replaced with something similar. I tried to work it though the gears to see if anything would bind but no matter what I did it never seemed to get into reverse despite having full range of motion in the neutral gate on the shift tower. I did remove the other cable from the shift tower but it seemed to move freely.. I'm open to suggestions.

1st Gear

2nd Gear

3rd Gear

4th Gear

5th Gear

Reverse

 

Reverse should be farther in on that shaft than 5th. On my car fifth is over and next to third but reverse is not directly behind it is offset some more. Try pushing the shaft a little farther in than when it goes into 5th and see if you can find reverse.

 

 

Andy.....my "reverse" is, in fact, straight down from 5th which is unlike yours. However, here's the good part....I finally got it into reverse. Both cables were disconnected from the transmission and thru numerous attempts of "working" the lower lever in conjunction with pushing/pulling the shaft that goes into the transmission, it finally...finally... did I mention finally?....clicked and went into reverse. The pic of shaft position is below. This leads to my next question: Does this now point to bad cables?

 

Please note that the "lever" that moves the shaft in and out was moved off to the side so I could get at the shaft bettern.

 

I bet your cables are still serviceable, in your first pictures the “lever” was in the wrong “slot”. I would look at the pin that is part of the lever and see if it is worn enough to let it slip to next slot. If so maybe a welding shop or a machine shop could replace the pin and solve the problems. Just thinking.

 

I'll take a look but I'm not sure on how that "lever" could be taken out by itself as it doesn't appear to be a mere bolt assembly holding it to the transmission. I'll need to take a closer look at the bottom to see how the pivot point (pin) is actually attached instead of just trying to feel my way underneath it. However, in theory, if I put all the cables back in place with the pin in the correct slot, should it not work? At least as a test?