Mac's in N.Y. lists a '55-57' T. Bird Fordomatic gear shift linkage Bushing-Washer kit, their #66-28337.  Would those parts be the same as a 57 Car?
I'm asking because I had a "misadventure" a year or so ago, where my 57 car while idling, "popped out of Park" into Reverse, leading to injury & some damage.. Later we tried to adjust it, with limited success.  It appears  the shift linkage is, not surprisingly, somewhat worn.. 


Paul

I am not familiar with the Thunderbird floor linkage but with a column if the the pawl gets rounded from use at all the column shifter up at the steering wheel it will slip out of park and into reverse. This was a major concern of Fords many years ago. The Cruise-O I have doesn’t have a detent in the transmission; it relies on the shifter arm to hold it in.
For this reason I set the parking brake every time I have the car running and I’m not behind the wheel. (Neutral too)
I have had my steering wheel off and the turn signal unit laid over to the side and had to file the edges sharp again. This is on a 56 which I’m sure is the same as a 57.
On the shifter linkage right at the firewall you can turn the adjustment one turn down to bring up the arm on the trans. There is a rubber bushing in that column arm that might be your problem. I bought a new one but don’t remember where. That long linkage to the trans does not have a bushing on the arm on the side of the trans.

56 Vic, B'Ville 200 MPH Club Member, So Cal.

Maybe this ILL will help ID what you need -

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7341 on the illustration is the black rubber grommet I bought.,

56 Vic, B'Ville 200 MPH Club Member, So Cal.