You may have a broken or loose fuel pump eccentric. It is on the front of the camshaft. It is a round piece that is offset on the cam so it can push the fuel pump arm up and down.
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67 Fastback - Arctic White Pearl paint
351W ,Trick Flow Aluminum Heads, Edelbrock TorkerII, Carter 750 CFM, Comp. Cam 477/510 219/233@.050, Performance Automatic C-4 Trans, 3.55 gears, Front Disc Brakes, 1-1/8" Fr. 3/4" rear sway bars.
My 351W Fastback