Cessna 402/402C/B379 Businessliner/Utiliner
Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Communication Breakdown; Situational Awareness; Time Pressure
Conflict Ground Conflict; Less Severe; Deviation / Discrepancy - Procedural Published Material / Policy; Ground Incursion Runway
Flight Crew Took Evasive Action
Human Factors
While back taxiing on runway XX at ZZZ Airport; another twin Cessna; Aircraft Y; announced a 1 mile final on runway XX and then stated that 'they had the aircraft lights in sight on the runway.' Before entering the runway; the First Officer had made several radio calls on CTAF announcing our position and intentions. At no point over the course of the time since we turned the avionics on to the back taxi on runway XX did we hear another aircraft make a radio call. When we entered runway XX to back taxi; both the FO (First Officer) and I checked left and right and did not see an aircraft on final for runway XX. As soon as we became aware of the aircraft on final for Runway XX; I quickly turned the airplane around and exited onto runway XY. Had I not had all aircraft lights on while taxiing; I believe there would have been a high likelihood of a runway incursion leading to an accident.Both the First Officer and I followed company SOP and adhered to all applicable regulations to avoid a runway incursion. I believe the cause and fault lies with the pilot of the other aircraft; Aircraft Y; who failed to monitor ZZZ CTAF and make appropriate radio calls. Additionally; he did not have the appropriate lights illuminated on his aircraft that would have alerted us to his position on final before we entered runway XX.
C402 Captain reported hearing an aircraft on final approach during back-taxi at non-towered airport.