What I can list as of now:
Newport (or Custom) 2dr ht: 3
New Yorker Brougham 2dr ht: 3
Newport (or Custom) 4dr sedan: 2
New Yorker Brougham 4dr sedan: 2
Town& Country: 3
I'm sure that there is more of these, but I can't remember them.
To me it looks like the reclining seat back mechanism, so when you pull the chromed lever up, the seat back may be pushed rearwards to the desired position.
I have no information about where it could be rebuilt.
PS, where are the head rests?