Before I replay I just realized (sorry) that this is your first thread - so welcome to the site and we hope that you find the information here useful in your concours restoration goals and projects
The latest videos suggest multiple issues
In the one it appears that the bell/upper housing is moving when compared to the shaft This might suggest that the attachment between the two are loose
As far as under the dash it appears that you have a collection of non factory parts
Your car (in this area) appears to be a collection of parts put together without much focus on originality Your car is in the upper left and it shows that the clamp has aluminum blocks like that used in 69 and the bracket appears to have been made for those style of attachments. In contrast the lower right picture below shows a factory 68 mount. The clamps/bracket and attachment hardware are different between the two
Think this is where some of the other play is coming from in your demonstration
Looks like now (if you haven't already) is a good time to pick up a copy of the assembly manual that covers this area or a shop manual so that you can get all the correct parts, look at exploded views to see how all of this goes together and you can figure out what is not tight where it should be. We can only provide possibilities you have to do the work
Again welcome to the site