Probably a Quadrajet??? If so the secondary's open by pressure differential or on demand so to speak. Glad you got it running, hope you can afford to feed it.
I have always been partial to the 350 but have had to make all of them work at one time or another.
I got a lot of them figured out so as to not waste much motion, just go straight to the problem but I really had strange one once that every one swore up and down the fuel pump (in the tank) had gone out.
That didn't make sense since was running (idle and rev up just fine)(fuel pressure up to speck for TBI) just would not always develop needed power. When you step down on it, it would pause and then put you in the back seat then cough and sputter and sometimes back fire through the Carburator (TBI).
Turned out to have a crack in the hose that connects the fuel pump to the fuel line. Fuel pump sits on the bottom of the tank so when the tank was full it did not leak so much to be a problem but the lower the fuel level got the more it would act up.
I guess I'm ramblin, Have a good one.