BRUSSELS — The police seek him in Spain. Journalists seek him in Belgium. His whereabouts usually remains a mystery, turning the exile of Carles Puigdemont, the once and would-still-be leader of Catalonia, into a real-life game of Where’s Waldo.

In November he surfaced in the Sonian Forest, a woodland near Brussels. Several days later he was spotted buying candy in Ghent, before re-emerging at the city’s opera house. Residents of a small village near the Dutch border were surprised to find him dining there. Then in January he turned up in Denmark for a day.

“To get the man in and out of a place where he could eat without being seen was a huge feat,” said Lorin Parys, a Belgian politician who has befriended him.

All of this points to the paradox of Mr. Puigdemont’s strange existence since he fled Spain for Belgium in October after the authorities disbanded his government and sought his arrest on charges of sedition for leading Catalonia’s independence drive.