Ok, so it's 2012 and I am just now watching Roswell. I'm having a marathon actually. In season 2 Alex played a very distictive Bass Guitar, Blonde in color and F-holed. In season 3, episode 8 Billy comes to visit Majandra and is tuning a Gibson 6 string acoustic guitar. Majandra gets mad that he is even touching it and takes it away. We find out that it was Alex's guitar and she does not want that memory violated.

I guess he could have had more than one guitar but from what I remember the only scenes with Alex and a guitar I saw was the bass with the F-hole.