Are you sure? The one in the Live in Dallas video has no control knob under the pickguard, this one does.
I'm fairly certain that the guitar from
Live In Dallas was his black Les Paul, which was THE primary guitar he used in his Morrissey years, at least from 1991-2002. It's notable for the on/off toggle shaped like a die - you can clearly see it when they were on Craig Kilborn in 2002, for instance - and less clearly in the pictures from the
Beethoven Was Deaf CD booklet. He had at least one more black Les Paul used in that era - virtually identical - which he shared a picture of on Facebook years ago. He also used a gold Les Paul frequently and has been seen using that in the rare live appearance since 2004 (e.g., a TV appearance with Anya Marina). He seemed to favor Telecasters for
YATQ/
ROTT/Red Lightning (as seen in
Who Put The M...), some speculating because they were lighter and caused his back less grief - anyone who plays guitar knows that Les Pauls weigh a ton. I believe he auctioned off a white Telecaster 2011-ish and the proceeds went to an animal charity of some kind (I could be mistaken). A few years ago he also auctioned off a Danelectro that he used as a warm-up/practice axe before Morrissey shows. For authenticity's sake, he posted a picture of a
Maladjusted-era Morrissey holding it.
A musician was attempting to get an interview show with LA musicians off the ground a few years ago and there are a handful of clips on YouTube showing Alain in his home studio showing off various guitars. He had a quite a few, one of which was probably the electric sitar heard on various
ROTT tracks. I recall another was the guitar he used to play "Meat Is Murder" live. I suspect with two kids now it's probably a case of him consolidating what he doesn't need or use regularly. It sure appears Alain is living quite well and very happily. Fatherhood seems to suit him.
EDIT:
The white Telecaster was sold in 2010 in support of Boxer Rescue LA:
http://www.morrissey-solo.com/article.pl?sid=10/10/29/1537212
The Danelectro Silvertone was sold in 2012:
http://www.morrissey-solo.com/content/875-Morrissey-Guitar-on-Ebay-owned-by-Alain-Whyte