TBM, Pretty sure my electric fuel pump is of the Facet type and seems to perform much as the old SU type in terms of the audable clicks in that if there is little or no fuel in the float bowl, the pump ticks rapidly until the floats close the needle valve in both carbs, after which the tick slows right down to a sort of slow and steady heartbeat until the engine is cranked and fires up..
Just thinking in type...and passing some time... (-:
mfg, being a modified car I guess there could be mods to the fuelling system incorporated from other Morgan models. With electric fuel pumps there have been a variety of safety features to inhibit the fuel continuing to be pumped out an open pipe after an accident if for any reason the ign is left switched on.... In my mid 80`s +8 there is an oil pressure switch in circuit and if the oil pressure drops the fuel pump is cut off. Thus imagine after a lengthy lay up, the battery is perhaps not at it`s best, the float bowl(s) are low or empty, and the fuel pump will not come on until the engine has been spun over to generate enough oil pressure to close the switch and liven up the pump all the time the engine requiring to be cranked until the pump has run long enough to fill the float bowls.... With luck the battery has enough to accomplish all that and generate a decent spark at the plugs, in order to get things going..???
It will be interesting to find out the cause of your particular problem..
Good luck.