#1
Does anyone know whether the Epi ES-339 Pro has a coil tap or split coil system?

Even the Epiphone site uses both terms interchangeably, so can't tell

FWIW, the single-coil pull mode genuinely sounds single coil, extra noise and the works.....
#2
It's a split. Actual coil taps are exceptionally rare, I can't think of a single production model that has a tap. Where they do exist is usually on single coil pickups anyway.