Looks like an Astatic 335H. A couple of yrs ago you could buy them on ebay all day long for $12 to $15. I've had a couple of them and didn't like them at all. Real thin tinny sound. Of course Billy can make it sound good.
Billy could make a tin can and a string sound elegant. He's bad ass. He frequently uses an Electro Voice 635A which sounds quite nice through that Peavey amp.
I think my drummer has that amp...they are cheap but hard to find on eBay...One more toy to add to the list...I can lineout right from my DT into that...would be monstrous...and heavy and cumbersome.
A solid state amp? Billy has been using one for years. Sugar Blue used to play through a Mesa Boogie during the 1980's. I've seen Carey Bell play through all sorts of amps that most people would never consider using as harp amps. Cotton and Junior Wells played through the PA as did a host of others.
The bottom line is you play through what you like. It may not always make sense to other players. Does it really matter what others think?