It may be that the cam lobe that triggers the mechanical fuel pump is worn. Would work fine when the engines running at normal revs. but not enough 'oomph' to prime the carbs at start up.
I had the same issue, so switched to an electric fuel pump mounted near the tank, and a malpassi filter king under the bonnet to make sure the correct pressure is being delivered. Now I turn the pump on, give it a few seconds to prime, couple of pumps of the accelerator and she starts fine. Facet fuel pumps click all the time though, so don't wait for it to stop ticking!
Have repurposed a dash switch to provide power to the pump (and an added security feature) and fitting an inertia switch just under the dash on the right hand side so I can reset it on the move if necessary.
