After you defeat the Elite Four and have all 16 badges, talk to Professor Oak in Pallet Town. He will give you Rock Climb (HM 08) which is necessary to access Mt. Silver.
Go through Route 22 to reach Mt. Silver. All you will need is rock climb to continue going up the mountain, and at the top will be Red.
You will be able to battle him again after you defeat the Elite Four once more. Keep defeating the Elite Four to continue battling Red.
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I don't think you can battle Gardenia in Pokemon HeartGold.
let your Pokemon battle
No they can't.
No, you can't battle Maylene and/or Crasher Wake in Heartgold.
To re battle red u must defeat the e4. After u beat the e4 red will reappear. do this as much as pleased