Why an airborne patrol did not reveal a carrier

Would running combat air patrol make the carrier easier for the enemy to locate?

Not reliably, because surface ships also launched spotting aircraft such as Swordfish, so an aircraft sighting did not identify a nearby carrier.

Keeping combat air patrol aloft would not necessarily make a carrier easier to find. An aircraft sighting did not identify its launching ship in this period. Surface combatants also flew spotting aircraft, and many battleships operating around Norway carried Swordfish. An enemy might know that an aircraft was nearby without learning whether it came from a carrier, a battleship, or another surface ship, so the defensive value of the patrol outweighed this limited disclosure.