Geegaw Hackwrench was the father of Gadget Hackwrench and a close friend of Monterey Jack. Though his only appearance in the whole show is limited to being mentioned and a picture of him in one episode which doesn't really make him a character, his importance for the fandom should not be underestimated.
Geegaw was a male mouse. His height remains unknown as he has never been seen together with any other character in the show. His fur and his moustache were about the same brown as Monty's, his face showed a brighter color.
He wore an aviator jacket, an aviator scarf and an aviator cap with a pair of goggles, the latter two quite similar to what Monty wears. So his outfit left no doubt about what he loved doing the most.
By the way, Geegaw was left-handed.
Monty referred to Geegaw as "the greatest pilot in aviation history", and a marvelous pilot he was. He had a plane of his own, the Screaming Eagle. He must have been quite an adventurer as well, flying around with his friend Monty, maybe even after Gadget was born. It is also likely that piloting was among the things he taught his daughter.
The way Gadget misses him gives the impression of him having been a wonderful father to her. And he was the forgiving kind—although he got angry about Monty when they were in Zanzibar, he left the Screaming Eagle behind when he went on his last journey, saying that Monty shall have it.
Though the old Disney comics, especially Chip 'n' Dale Rescue Rangers 17, say something different, Geegaw has never been an inventor. If he had been one, Gadget wouldn't have had to gain her engineering knowledge all by herself.
In To the Rescue (Part 3), the "Rescue Rangers to be" had to fly to Glacier Bay somehow. So Monty led them to the old bomber plane in which Geegaw used to live with his daughter Gadget. But when they discovered that he wasn't there, Gadget told them that he won't come back and that she had lost him one year ago. This leaves his fate mostly unknown.
Technically, Geegaw doesn't appear in the show at all. However, in To the Rescue (Part 3), he is talked about by the Rangers to be, and his picture is shown.
Accepted Fan Fiction Conventions
What happened to Geegaw Hackwrench? This question is definitely one of the most interesting issues from the TV show dealt with in fan fiction. The most usual version of his fate is that he died in a plane crash, allowing him to appear in prequels and flashbacks only. But some fan fiction authors refused to believe that he lost his life and had him return and meet the Rescue Rangers.
Closely linked to Geegaw's fate in fan fiction is the fate of Gadget's mother who has never been mentioned in the series. The fates of both in different fan fiction universes can be found on the page about Gadget's family.