Dampé?

Dampe is a male, Hylian, gravedigger who appears in a few of the Zelda games. He appears in such games as "The Legend of Zelda: Ocarina of Time" and "The Legend of Zelda: A Link Between Worlds", he is not classified as a main character, more of a side character who sometimes has a big part in the story. In "A Link Between Worlds" You have to visit Dampe to actually carry on with the story so he sometimes has a fairly big part or he is just someone you can talk to optionally. He doesn't tend to change in his appearance or what he does, he will always be a elderly man working at a graveyard (quite sad if you think about it.) In "Ocarina of Time" Dampe can be found in the Kakariko Village Graveyard (Which also appears in "The Legend of Zelda: Twilight Princess") where he starts a gravedigging tour for 10 rupees while Link is a child, where he digs up items which Link can keep. Such as rupees or heart pieces. Also, at night, Link is able to read his diary to find treasure, and Dampe will find out and give him the treasure. Keep in mind, when Link is an adult Dampe's diary will say something different than what it did when Link was a child.

Dampe has also appeared in "Majora's Mask" where he can be found in "Ikana's Graveyard" which is haunted. At night on the final day, he is beneath the graveyard searching for treasure but he can't see since he lost his lantern. But your fairy, "Tatl" is like a light so he asks if Link can come with him with the fairy and guide him. Link ends up getting the treasure since a "poe" / ghost appears and he defeats it, as Dampe runs away.

In "A Link Between Worlds" Dampe isn't looking for treasure, instead he is doing his job properly and is looking after the priests daughter.