You cant fight him. You can only use that GYM for rematching gym leaders.
Uhh the person who wrote that ^ up there is wrong. He is in in Mt. Mortar like in Gold and Silver. You battle him and he uses a Hitmonlee and Hitmonchan, if you have empty space in your Pokemon whatever then he will give you a Tyrogue.
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You will find him in Mt.Mortar. Pokemon Ace Trainers Ace Trainer Olivia
The Fighting Dojo Master is in Mount Mortar in the Johto Region. There are three entrances between Mahogany and Ecruteak, so take the middle entrance (and have rock climb and surf) to get to the dojo master.
Deep within mount mortar. hint: you have to use the middle entrance
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.
In Pokémon Gold, the fighting dojo master is originally found in Mt. Mortar. He uses a Hitmonchan and a Hitmonlee.