Here is the video after I installed it with the bushing. It absolutely does not move as much as before. I did notice that the transmission mount does move at the red mark. I also hear a clunking sound coming from the tail housing or the shifter:
Sorry for the wind.

 

I think that hole on the bottom is probably correct, not sure though.   Might not matter.  Maybe the top lets fluid in?  Maybe the bottom lets it out?  p.s. I did a Google and found this, which makes sense.  Your 4 speed probably doesn't have an "oil supply" groove so it probably doesn't matter.  https://www.allfordmustangs.com/threads/t5-tailshaft-bushing-oil-hole-orientation.327137/

How about vibration?  One reason I didn't think it was the bushing was because of the vibration that you'd expect if it was so loose that the seal couldn't seal.  But, apparently I was wrong.

That's a lot of movement, you'd expect the yoke to be rattling around in there when the car is moving. 

Edited February 14, 20214 yr by Zed Head

During my drive I was feeling the shifter every now and then in different gears. I would say at most there was what I would describe as a buzz rather than a vibration. (I think vibrations as a little more violent.) 
I guess the seal was doing just barely a good enough job of preventing the rattle. Obviously didn't prevent the leak without the help from a bushing.

Might be that the splines alone (inside the yoke) were enough to stop the serious vibration but the seal movement outside was too much.

Thanks to the guys that found that Omega bushing.  I had never actually seen it.  They call it out specifically for the 71C but it looks like Nissan used the same dimensions all the way back to 71B, at least.

So, the last questions is - what the heck happened to the original bushing?  

13 minutes ago, Zed Head said:

So, the last questions is - what the heck happened to the original bushing?  

¯\_(ツ)_/¯

I bought it from someone in New Jersey. He bought it from someone in Kentucky. They used it for drag racing. It used to have a 6 point roll cage. It now only has 4 points with the two  going to the footwells removed. 
There were many things in this car that were butchered or slapped together haphazardly.  Example : They cut the springs all around to lower it. If you lifted the car you were able to rotate the springs by hand.
So who knows if this person just said f' it when rebuilding the transmission (if it was rebuilt) and left the bushing out, or something entirely different.

 

I wanna say thank you to everyone that was here and helped me out. Y'all are great.

Good to hear you have solved your leak. The omega bushing works in the 71B 5 speeds, I know that for a fact as I used it in 2012 and it is still working fine.

Looks like it's a good replacement for the 71B 4 speed. Thanks for the feedback.

Double post.

Edited February 15, 20214 yr by EuroDat
Doible post