Jerry isn't playing a Del Vecchio, it's missing the label on the headstock. I think it's one of his Baldwins. You can see the volume knob on the side of the guitar that he had installed on all of his Baldwins.

I also don't think it's Jerry playing when Merle starts off. It sounds that it's only Chet and Merle playing, so I'm guessing Chet is playing rhythm.