Help me ID this BW "T96-1B" trans application

I have this trans that a friend gave me. He thought it was from a Ford or Mercury, but could not remember. I know form the casting numbers it is a Borg Warner, model T96-1B from the casting numbers. I know it is a three speed OD, and has the flanged output shaft, not a sliding yoke. The inside is nice and good condition after removing the top cover. What is the rear cylinder up top? It rotates some with the output turning, beats me what it is? I am pretty sure the side round cylinder is the OD solenoid, right? I am a real neophyte on these old transmissions, I am sure the HAMB expertise can help.

What I need to know, do any of you know the original use for this transmission? I plan to take it to Turlock swap to sell and would be nice to know more about it to help answer any questions. I appreciate your help. Couple quick pics to aid the questions. Thanks, Terry

 

Rambler?

 

I forgot to also add there is a small lever, behind the OD solenoid, that is on the small bump on the tailshaft. Looks like a bolt in the picture. It rotates 90 degress, what the hell does it do?

Flipper, your guess is good as any I have.......

 

No, Rambler used a torque tube through 1966. It's quite like one I had out of a Studebaker.

 

Actually my '64 Rambler had/has an open driveshaft. It depended on which model - certain years - had both - '64 had both open drive shafts as well as torque tubes.

 

its out of a early rambler american and the little lever is to ingage the over drive

 

Thanks for the info from everyone, especially clays diff. Terry