I dont believe most electrical components would cause it to shut off unexpectedly. it may cause it to spit and sputter but not randomly cut off. its kinda like taking your battery out while its running... itll still run because of the alternator ( assuming your alternator is good). chevy is notorious for fuel pumps. mine is a 2000 and if i keep it above 1/2 tank, it'll never happen. but as soon as i get down to about 1/4 tank, it'll do it at random ever 5-15 minutes. if your oil pressure is reading zero i think thats a little bit bigger of a problem to focus on before worrying about why it keeps randomly cutting off. i would focus my attention on that first