My fuel pump is a Facet, mounted in the engine bay, and can be heard ticking when the ignition is first switched on, as the carbs fill. After that, in normal running it will 'tick; very slowly as it sends fuel to the carbs.
When vapourisation occurs, it will 'tick' frantically, at full speed, as it trues to pump vapour. Before Icured it for once and all, as noted above, thsi ticking was a warning of vapourisation starting..
NB. over fitted a return fuel line from Carbs to tank, to re-circulate fuel in an attempt to cure vapourisation. if this is still in place on your car, the fuel pump will run continuously, vapourisation or not. Re-circ. pipe runs from the RH carb float chamber back to the tank. It might have been blocked. off when the electric pump was fitted.
Dos your pump use the reserve feature? If so it might be an older Solex pump, perhaps fitted to P4's, and NLA. Facet pumps are single inlet and single outlet, more normally fitted in engine bay. Technically these are "Long suck, short blow" pumps. Pump near the fuel ank is a "short suck, long blow" pump.