Well, the 16th gym leader is Gary. His gym is located in Viridian City. In order to enter, you need to have met Gary (Blue) on Cinnabar Island and spoken to him. Once you have spoken to him, he will teleport (presumably using his Alakazam) back to his gym, where he will be waiting to battle you.
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The 6th gym (Steel type) does not unlock any new HM , instead the 16th Gym (Blue's Gym) unlocks Rock Climb
After you beat Blue, the 16th gym leader
defeat brock blaine misty ericka poison leader and all the other gym leaders
To get Rock Climb, you should have all 16 badges and when you step out Blue's Gym (16th Gym Leader), Prof. Oak will call and will tell you to go to him and when go to his lab, he will give Rock Climb.
If HM8 is Rock climb, You have to beat blue (gary Oak) then talk to Prof oak and he give you it. Blue is the 16th Gym leader