BE-300 pilot reported a landing gear indication malfunction while on final approach in visual conditions. The pilot performed a go around; manually extended the landing gear; then landed and stopped on the runway.

Narrative

On the visual approach to Runway XX in ZZZ after putting the gear down on approach to landing; the right landing gear light on the gear light enunciator did not illuminate. After a brief discussion; the crew contacted Tower and made them aware of the issue. The crew decided to continue the approach and fly over the field to have Tower visually inspect the gear position. The crew briefed a normal missed approach with the exception of the gear remaining in the down position. Tower indicated the gear appeared to be in the down position. The crew was instructed to fly the published missed approach up to 4000; but was subsequently given a heading of 210. After completing the missed approach with associated checklist; the crew requested vectors to the north of the airport to troubleshoot the issue. Departure gave instruction to climb to 7000. At this point; the pilot monitoring (PM) made the passenger aware of the situation and briefed them on the intention of the crew to troubleshoot.Troubleshooting to determine gear down included pushing the Gear Indicator Light Housing and determining bulb operation. Reducing power below 85% N1 without a gear horn aural warning. lowering flaps beyond approach position with NO aural warning. No red handle in transit light. The light remained extinguished after the handle was placed in the down position. While on a heading given by ATC; the crew advised departure of the inability to climb to 7000 due to drag from the gear. The PM attempted to eliminate the possibility of a light bulb issue by replacing the right main gear light bulb per a conversation with Maintenance. After replacing both the left and the right gear indication lights; both did not illuminate. There was a discussion between the PM and Maintenance and it was decided as a crew to complete the Manual Landing Gear Extension checklist. The crew followed the checklist which instructed first to pull the landing gear circuit breaker relay. The crew then completed the checklist items which instructed hand pumping the gear down with the emergency gear extension handle. The pilot flying (PF); with positive exchange of controls to the PM; hand pumped the gear extension handle for approximately two minutes with no change in indication or hydraulic tension in the handle. The crew made the decision for the PM to land the plane from the right seat while the PF pumped the manual extension handle before landing; per the associated checklist. The crew [requested priority handling] with Departure and noted fuel and SOB (Souls on Board) before receiving vectors for the visual approach to Runway XX. The PF made a normal approach to landing and stopped on the runway. The crew then completed the engine securing checklist and shut down the aircraft on the runway. The passenger was directed to exit the aircraft with the maintenance team. The aircraft was towed from the runway by the maintenance team.