Bad timing doesn't start right up, run a minute and die. It's got to be the carb or pump. (fuel supply issue of some kind) provided it's not a bad ignition switch. You can put a jumper, with an alligator clip, from battery to coil.
This is the page you can use to determine what kit to buy.
And this info from his site: "The Rochester 1 barrel used a small metal tag attached to one of the float bowl screws for identification. When the tag is missing, check the bottom of the mounting pad. If you find 4 numbers add 700 to the front of the 4 numbers and that will give you the carburetor number.
Carburetor kits contain gaskets, needle & seat, accelerator pump (some are pump cup replacements) and other various parts. The K1144 is for the earlier carburetors that use the flat stem accelerator pump. This is a leather pump cup, which was standard. The other kits are for the later model Rochester B carburetor and they usually contain a replacement rubber cup. These were used on round stemmed accelerator pumps that uses replaceable cups."
I notice the Carter Carb says 54-59? You have a 60. Probably no big deal, just saying. His 60-62 Carb is REME637. But his rebuild kit for Rochester 6 Cyl is for 1950-62.
Email Mike's Carburetors and he will set you straight. Send pics and all available info. Start taking carb apart with pictures and notes and clean it all out while you wait for a kit. J. Carter's vendor builder may have had some bad help that day.
I don't have an answer why you did not fix it though. Check ball left out or stuck in hole is all I can think of that a builder would screw up. Warped housings maybe. You need to take it apart and carefully examine to see all the parts are there, clean passages and maybe discover something. Be careful to observe and keep track of EXACTLY what ball was installed in what location. There are different sizes and different materials. Aluminum and SS. Be sure to document how everything was assembled. You could find a gremlin and be on your way. your carb certainly looks worth "fixing"/recalibrating.
Mike Carburetors has a video on your B model. It shows disassembly and assembly. Everything you want to know is in the video. He mentions that if the float drags in the sides of bowl it will hang up and cause flooding, So center the float within the bowl when dropping in. This is a MUST WATCH video.
Again, be sure your pump is not over pressuring. Assume it's not electric and is a direct replacement mechanical pump for 1960 235. I think I do see it and it is Kosher.
