PA-34 pilot reported a gear unsafe" indication upon landing gear extension during approach. Pilot performed a go-around and completed a landing with all landing gear remaining down."

Narrative

On initial gear extension; 'gear unsafe' light illuminated and did not get any green gear lights to illuminate. Executed a go-around at approximately 1000 ft. AGL. Once at a safe altitude and in level flight; referenced the POH and performed the 'Landing gear unsafe' checklist. After performing the checklist; I was faced with a left main gear unsafe indication; right main and nose indicated safe. I elected to contact ZZZ Approach to perform a fly by with the tower to visually check my left main gear. They verbally confirmed the left main was down but could not confirm (nor would I expect) that the gear was locked. Having already [requested priority handling]; they suggested I land at ZZZ1. However; based on Runway XX at ZZZ and the unobstructed grass on the left side of the runway; I elected to land with the left-wing overhanging the grass. This scenario allowed that if the left main collapsed; the left wing would be in the grass and not potentially rupture the wing tank and create friction of metal on cement. Fortunately; the gear was down and the landing uneventful. Due to an unsafe gear indication; I stopped straight ahead and shut down the airplane. On visual inspection; the gear was not locked but was down; thus a turn to the right may have caused the gear to 'fold' up under the left wing.Although emergency resources were more available at ZZZ1; my decision to go to ZZZ was grounded in the clear (no lights or obstruction) alongside Runway XX/XY. I maintained my [priority] status with ZZZ Approach until safely on the ground at ZZZ.