How to keep fuel up to the curb after shut off.

Happy T-day to you too!

How long is 'a while'? Minutes or hours or days? Is this a stock type mechanical fuel pump? What engine: small or big block? Carb?

The mechanical fuel pumps have 2 check valves in them; 1 at the inlet and 1 at the outlet. You could very easily have bad or dirty check valve in the fuel pump.

1. Run the engine for a little bit (not too warm), shut off wait for about 5 minutes, then crack the fuel line to the carb; it ought to still have plenty of pressure in it. (OR, tee a pressure gauge into the fuel line to the carb and watch the pressure after the engine is shut off; it should stay steady for many, many minutes.)
2. After shut off, pull the air cleaner and look down into the carb without moving the throttle. There should be no fuel leaking into the carb throat.
3. Smell the oil to see if there is any odor of gasoline in it. If so, then a carb leak or a leaking fuel pump diaphragm is the cause. Needs to be fixed PRONTO before the oil gets diluted with gas; and if it is a carb leak, it is washing down cylinders with gas.