Location: Indigo Plateau
Unlike both Blue & Green, Red is not found multiple times. Instead, Red will only appear when you have reached certain conditions. To get to Red, you need to beat at least 6 Master Trainers. This shows that you have a team of 6 worthy Pokémon as Red will only battle you if you have 6 Pokémon on your team. When that is done, he will appear outside the Pokémon League in the Indigo Plateau.
Defeat him and you'll earn the special title of Battle Master and will then leave. He re-appears when you defeat the Elite Four once again