I assume this gun operates such that the recoil from the first shot switches it over to fire the 2nd barrel. I can't fire it here and with snap caps it doesn't switch.

It is, indeed, a recoil actuated trigger. Dry fire the first barrel and then give the butt a good rap with your open hand. If that doesn’t set the 2 second barrel then tap the butt on a carpeted floor. That should do it. Japanese SKB triggers are very reliable.

I would not recommend rapping a SKB 150 butt on a carpeted floor.
Lovely guns as they are, it is very common to see cracks in the butt stock, originating at the points of the scalloped frame.