Thanks, Grigg. I was kind of wondering. It doesn't appear to be the original carburetor, for one thing, and it isn't all there for another, but as long as I kept pumping the accelerator it would run.
I have two Rochester Bs laying around, one freshly rebuilt. I guess I'll just pop one on and get rid of that other carb, which I hadn't planned on keeping anyway.
I can hang the Briggs and Stratton tank from the inside of the hood until I figure out where the real problem is.