He is said to be at the deepest part of Mt. Mortar. I haven't tried to find him though, as I really have no interest in battling him or anything.
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In Pokémon Gold, the fighting dojo master is originally found in Mt. Mortar. He uses a Hitmonchan and a Hitmonlee.
You can't get the badge to the fighting gym. You can however, fight the dojo master. He is in Mt. Mortar. When you beat him, he will give you a Tyrogue.
In Pokemon Gold, Silver, Crystal, HeartGold and SoulSilver the Fighting Dojo Master can be found in Mt. Mortar. He is found deep in the mountain past a maze. Try to have an empty slot in your party as he will give you a Tyrogue for defeating him.
He is very deep in Mt. Mortar
He won't come out.