cut out being all electrics or just engine?
the factory immob is known to be iffy at this age. like you say fuel cut off. also check the spades, as they could be corroded.
you can also check for a vacuum in the tank, just take the cap off when it happens and listen for air going in.
lift pump may be going, clogged filters, engine side or tank.
on the air side check for delaminated pipes causing a restriction when the revs are high