'54 / '55 Fordomatic ID ?

[dmsfrr]

I have an air-cooled Fordomatic in a '55 Bird that the transmission rebuild shop said is a two speed. When driving or being manually shifted it only shifts one time.
It was my understanding the original air-cooled auto trans for a '55 Bird 'should' be a 3 speed that normally just skips first gear unless manually shifted, or kicked down. Same with the '56 & '57 Ford-o transmissions.

But, the transmission info at this link says the automatic is two speed, and the same for '56 & '57 Birds. http://automotivemileposts.com/tbird/prod1955tbird.html
I'm confused.

Was the '54 Fordomatic a two speed? How would I easily tell them apart if they're different from the air-cooled '55 version?
I remember the ID tag on the trans being blank when I was looking at it a few years back.
Are there other numbers or letters cast into the trans that would be different?
The car had a '54 engine when I got it and the transmission may(?) have come with the engine.

OR, am I lost and barking up the wrong tree?
.