I tend to agree with your mechanic that this sounds electrical. I am somewhat familiar with this body type but only from '72 back. However, "assuming" that you have the Transistor Controlled Switching" unit that actually controlls the firing of the coil you might want to have that checked. It "should/may" be located under the battery and just behind the headlights on the drivers side. Check to see that the ground wires from the distributor and condensor are in good shape. Corrosion caused by battery acid can attack the connectors on the TCS unit and this could cause what you are seeing. Also, make sure that you have good wiring from the ignition ballast resistors (should be two of them) to the TCS and back to the Coil. Might check the ballast resistors with an Ohmmeter.
My experience with the fuel shut-off solonoids is that if they fail then you get a car that won't idle (rock-n-roll) but runs "OK" at speed (since the idle circuit is out of the loop at that point). You can start a car with the solonoid(s) bad (or if the fuse is blown) but you can't keep it running except with a lot of throttle. You will recognize this condition if/when you ever experience it.
I basically made mine into "dummies" so I don't have to face this problem again.
Anyhow, I think you need to take a good look at the electricals.
Fuel pump?? Dunno, I would think that if the fuel pump was bad your engine would not just quit without going thru the usual "help, I'm running out of gas symptoms".
Dan Taylor/ Tulsa, OK MBCA
'84 300D/'90 Jaguar XJ6/XJ40