Small, warm-seeking, and closer than you think
A leopard gecko is a few inches of nocturnal ground-dweller, and his escape radius is modest: he walks the floor at night, takes the first warm, dark, snug gap he finds, and sleeps the day away inside it. Under the refrigerator, behind the warm back of a dishwasher, inside the toe of a shoe — these are palaces to him. Most leopard geckos are recovered in the room they escaped in or the one beside it, and the search succeeds on thoroughness at ankle height rather than on covering the whole house.
Close the room's door, get other pets out of it, and warn everyone in the house to check shoes before putting them on and to watch where they step after dark.
The floor-level search, done properly
Do this on your knees with a flashlight, in the late evening when he is likeliest to be out, and again in daylight for the sleeping spots. Work the room's perimeter inch by inch: under and behind every appliance, inside the gaps under kitchen cabinets where the kickboards leave a hollow, behind storage boxes and books stacked on the floor, inside boots, shoes, and bags. Leopard geckos squeeze flatter than their round bellies suggest, and a sleeping gecko in shadow is the color of dust and carpet combined, so sweep the beam slowly and look for the spotted pattern rather than a shape.
Check inside the enclosure stand and any furniture with a hollow base, and lift floor-level items out of the room as you clear them. Move furniture slowly and straight out from the wall — a gecko sheltering behind a bookcase is exactly where a dragging leg lands.
A warm hide beats a chase
Chasing a sighting across a room rarely ends in a capture and often ends in a dropped tail, so trap with comfort instead. Put his own warm hide on the floor against the wall nearest the enclosure — the hide carries his scent and his exact idea of safety — with a shallow water dish and a small straight-sided bowl holding a few mealworms beside it. Add gentle warmth under one side of the hide if you can do it safely with his usual heat mat. Dim the room and leave it alone; check the hide quietly with a flashlight every couple of hours through the evening. A gecko who has spent a cold day in a wall gap will relocate to the one warm, familiar-smelling cave on offer.
Hands off the tail
When you find him, slide a hand in front of him and let him walk onto it, or coax him into a low tub with a gentle guide from behind. Never pick him up by the tail and never grab at it to stop an escape: a leopard gecko's tail detaches as a defense, and while it regrows, the replacement is a plainer, costlier copy grown at real expense to his reserves. Expect a found gecko to be cold, hungry, and dusty rather than injured; offer water first back in the enclosure, then food once he has warmed.
Afterward, find the gap honestly — leopard geckos climb rough surfaces better than their reputation admits and push through feeding doors and cable gaps that look sealed. If the search runs past a couple of nights with no sign, the possibility he reached a vent or an open door grows, and neighbors become part of the search: KinsLe's Lost Pet Alert System lets a finder message you directly through his profile, so a gecko spotted under a neighbor's porch light comes home instead of being mistaken for a wild lizard.