[LiAm84]

Thanks for posting this video. IJ sure looks like he is having fun. He sounds great.
Illinois Jacquet plays a great solo on Cottontail with Lincoln Center Jazz Orchestra on the album 'Live In Swing City- Swingin' With Duke'. I'd had never really listened to him much until I heard this solo. He plays some really great lines and his tone is massive. The album is on spotify if you want to check it out?
I spoke to Scott Hamilton last year and he mentioned how much he really admired Illinois Jacquet, especially in IJ's later years.
Sorry to mention horns but it looks from pictures like he in fact played a SBA not a BA. Would also be nice to know what size tip he played on his refaced tone master.

 

[LiAm84]

I did some further checking on the sax pictures of IJ and think it's a BA, like sideC also mentioned in one of his posts.

Please check this picture (posted in this thread #10):
http://upload.wikimedia.org/wikipedia/commons/3/3d/Illinoisjacquet.jpg

When you blow it up to super size you can see in the right bottom (on the bell) a serial number. For me it's 29166 or something close to that. That number is listed as a Balanced Action of around 1939 in the Selmer serial number chards:
http://saxofoons.volop.info/serienummers-selmer

One of the striking differences is that BA's have the serial number on the bell and SBA's under the thumbrest, so that also makes this one probably a BA.

You are right about that picture. It is a BA. But that isn't the horn that Illinois Jacquet played in latter years... for example in the video you posted he is playing a SBA which you can distinguish by the adjustable Gsharp and longer bow compared to a BA. See following picture:

 

[LiAm84]

I also found some pictures of Illinois Jacquet with his BA and Conn 30m:

Seems like he started on a Conn 30m, then Selmer BA, then the Selmer SBA, and finally the super 80 series II.