It's been a while since I've done this but the phone call went something like this,
Me "I just purchased a T-Mobile phone from a friend and I'd like to unlock it."
CSR "Looking at your account I can't see that this devices has ever been used with one of your SIMs."
Me, "Just a minute." Quickly insert SIM in new phone and power up. "There is that better?"
CSR, "Oh, yes I see it now. I'll submit the unlock request. You should get an e-mail with the code within a week."
The old rule was that you were allowed two unlocks per year, per line. Not sure what the deal is today. YMMV
The phone may still have to show the minimum usage on your account in the unlock requirements.