I'm pretty sure it's an old (mid-fifties?) Gretsch Synchromatic. If you watch the video, and you're able to pause it on one of the shots of the guitar's head, you can see (although kinda blurry) the "Synchromatic"-logo across the headstock. I found this one on gbase.com:
http://www.gbase.com/Stores/Gear/GearDetails.aspx?Item=1869728
It's pretty much identical (except from the pickup, pickguard and the tailpiece) to the one that Brian plays in the video. They also made/make these guitars with "cats eye"-holes instead of regular f-holes, like on the Jimmie Vaughan signature model.