I just bought a 63 Falcon with the 140 i6. It runs and drives great except when under light acceleration; it bogs down a little bit and the engine speed fluctuates (sounding like I'm modulating the gas pedal). While it's doing this, however, if I really step on it, everything smooths out and it accelerates normally. The (2 speed auto) transmission also takes a long time to shift up, much longer than in my dad's 65 Mustang, which leads me to believe that it may be a vacuum leak. Is this a reasonable assumption? If not, what else could it possibly be?

Thanks so much!

 

Late reply but my 63 Fairlane had the late shift issue as well, would rev really high before shifting. Mine turned out to be the transmission modulator and I also replaced the fluid with Ford ATF, seemed to solve the problem. Good luck.

 

Something to check,
The gas in those days did not have the usual unleaded variety and if the needle and seat in the carburetor are of the old original vintage the unleaded gas could have caused the rubber tip on the needle to swell and affect the carb float level which could produce the lean operating condition you are seeing.
The top of the carb will need to be removed and the float level checked to confirm if this is the problem. Usually this spec info is available in some carb kits.
Had a 62 Falcon 4 door ,one of the best cars I ever had. Did not have power steering, but drove and handled like it did. Very reliable even if it blew a lot of fumes out the road draft tube, common problem ,soft rings & block.