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It looks like something is not connected at the very back of my transmission...
That hoizontal piece terminates in a coupling that is empty (except for gumpta)

Your transmission was either converted to a side shift and they didn't replace the tail shift nose cone, or the side shift cone was replaced with a tail shift version due to some sort of damage.

It looks like a tail shift transmission that was converted to Side shift
however they did not change out the rear tail cover when they did this

so the disconnected linkage is the old linkage that is likely not connected internally in any way

does it wiggle loose... when you turn the tail input shaft by hand?

Interesting. It doesn't budge by hand (I didn't put a tool on it).
Thanks for the info!

It could of been a damaged rear tail cone.

but if your car is a 1971
then someone updated it to side shifter
and didn't bother to change out the tail
you can buy a SS tail for it and easily change it in the car
or not....

Thank you sir!

That area above the plate on the bottom of the cover is loaded with gear lube. Looks like an attempt to stop a leak was done with RTV. There is a correct gasket for that task. The cover may be distorted too.

What I have done when I convert a Tail shifter to a side shifter and don't have a rear side shifter case I don't install the tail internal linkage and seal the long tail linkage holder with some JB weld and a freeze plug.