Steels that weld will dang near weld themselves when the conditions are correct. All the smith is really doing is getting the steels to the correct conditions then seeing to it that they come in contact so they will weld to each other. 5160 is not a real good choice for this, it is hard to weld because of the alloy elements; it is seldom seen in any pattern welded steel. 1084/15N20, 1095/L6 or 15N20, O-1/L6 are good combos because of hardening temps being similar. One can also use a hardenable steel and a mild steel like 1018. This is actually closer to ancient damascus mixing a hardenable steel for edge characteristics and a mild steel for strength.
One of the best tricks to use is to glance occasionally at the billet in the forge. When the flux starts to bubble vigorously, it is at welding temp. Heat the steel to red, flux, return to forge and bring to welding temp. When flux is boiling, remove and tap as you've stated.
When folding, heat to temp while fluxed. Remove from forge and scrub surface with a steel brush. Flux. Immediately fold over, re-flux, and return to forge. When flux boils, remove and tap-weld.
Good luck, hope this makes sense! I know what to do, but can't always convey it in words.