Gan Gogh is a one-off character from The Light Fantastic (EP187). He's best known for his obsession with capturing the Rainbow Lights—a rare natural phenomenon that occurs only once every twelve years near the ruins of the Remoraidians.
His whole thing is kind of tragic in a funny way. Years ago, he was just a traveling Trainer when he first witnessed the lights, and he became determined to draw them. His first attempt used seven crayons, which obviously wasn't enough to match the wild spectrum he was seeing. Twelve years later, he tried again with twelve crayons. Still no luck. Then another twelve years passed, and he finally showed up with 251 crayons ready to go—except that was the problem. He spent so much time deciding which crayon to use that the lights faded before he could even start.
By the time Ash and his friends meet him, Gan Gogh's given up on actually painting the lights. Instead, he guides them to the dried-up Remoraid Lake, convinced there's something special about the place. He's right. During their visit, his Venusaur helps take down Team Rocket after one of their usual Pikachu-stealing schemes. At sunrise, the mystery finally gets solved: Remoraid living beneath the lake are responsible for the lights, and they surface only once every twelve years.
In the end, Gan Gogh never does get his painting done, but he seems fine with it. Learning the truth about what causes the lights is enough for him.
One oddball detail: despite doing all his work with crayons, he keeps a paintbrush tucked behind his ear.
Content compiled by AnimeList.moe from publicly available sources.