Ok, so this isn't a new carburetor but a rebuilt one that is new to the gentleman who owns the truck. That could be problem number one. And it runs without stopping after it starts but stumbles and won't pump fuel into the manifold to make it start. First off, I would be highly suspect of any Rochester B or BC carburetor bought through any flaps. They all get their mdse from commercial or independent rebuilders. If you are curious about how these rebuilders work, please call CarbKing and ask him. The story isn't pretty. If you want to see what I discovered in opening 5 of these up a couple of years ago (and posted here), please read that stuff again. There was nothing that would make you want to buy anything but an NOS Rochester. That is if a Rochester is indeed what you want to use. Personally I'll say I tried hard to be as objective and positive minded as I could be about them, but with the fuel we get today, I agree 100% with Jon...hire a 15 year old to stand on the running board and pour fuel into the manifold from a leaking boot.
Here is what I'd suggest doing: get a carburetor rebuilding kit from Jon (CarbKing). The Rochester you have may be a mongrel (I would bet large that it is), but he'll be able to send what you need. Check everything in the carburetor...not just the float level, but the power piston, all the vacuum tubes, whether passages are open, what kind of accelerator pump the "rebuilder" used, etc, etc. Also see what size jet was used (could be any size at all). Stumbling can also be caused by no choke and an engine which hasn't warmed up yet...although in San Antonio, it ought to warm up enough pretty quickly. Please let me know if you need rebuilding specs. As for the vacuum advance, I'd remove the line from the carb and suck on it while watching. You ought to be able to make the dist plate move without too much effort. If that isn't happening, something is wrong either with the advance, the way it connects to the distributor or...the carburetor. Since I have no earthly idea who worked on the Rochester, there isn't any way to know if they even checked the vacuum passages. I've seen them rusted completely shut and I know Jon has also.