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Today I bought a 1962 Thunderbird to go with the 1991, 2000 and 2002 Corvettes. It is a nicely restored car, but does not drive anything like a Corvette. This is just as I got it home today, before any clean up.
Note to corvetteronw. To answer your question, look at the base of the steering column.
'birds with the swing-a-way columns have a rectangular opening at the base of the column with a cover plate that moved with the column (similar to the track around the park brake lever on the early C3s).
IIRC my T-bird history, the swing-a-way column appeared on the next-gen body in '64. I can't remember ever seeing any '63s with that column. The next-gen 'birds also had the sequential rear turn signals that appeared in either '64 or '65.
The '61-'63 cars were nicknamed "rocket birds" because of their profile (another bit of useless trivia).
Jonathan.....
BTW my grandmother's youngest sister had a red '61 when I was a little boy. Cool car.
Had a 66 years ago that had the swing away...so 66 was the last year for that as my 67 that I still have (grandparents bought it new in October 66) has the "tilt away" option. It is different because it tilts up and to the right rather than sliding through that rectangle in the dash like the 66.
Nice T-Bird. I'm partial to them also, have a 94 I bought in 95. That's got the IRS in it and it likes curvy roads. A little story, many years back I was on a curvy road with a lot of close corners/turns in it. Had a C2 come up behind me and he could not keep up with me through the curves till finally got to a long straightaway at which time he blew me off. Till that straightaway he had a hard time keeping up with me. Not too bad considering it has a 4.6 V8 in it.
As an aside, I was at the Concours at Ault Park in Cincinnati 2015 where they were celebrating 60yrs of T-birds. One of the entrants was a '60 set up to NASCAR super speedway specs by one of the race teams back in the day.
It was a solid-lifter 390 Interceptor engine with a 3-speed column shifted manual trans. This is the only manual trans 4-seat 'bird I've ever seen.
Had a 66 years ago that had the swing away...so 66 was the last year for that as my 67 that I still have (grandparents bought it new in October 66) has the "tilt away" option. It is different because it tilts up and to the right rather than sliding through that rectangle in the dash like the 66.
The Tilt-Away column was also available in '67-'68 Cougars and, according to urban legend, a few Mustangs.
New car
congrats! 
. It have the 390?