The Body Gear Steering is automatic on the 747-400, it gets enabled/ disabled around 20kts. And yes, it steers in the opposite direction being on the opposite side of the center point of the turn as compared to the nose wheel. Imagine if you steered right in a car and your rear wheels turned (swiveled) right, the front of your car would probably turn left!
The -200/300 had a guarded toggle switch which the pilot flying would typically reach out and enable/disable before the RWY exit/before takeoff.
I have been observer on a 747-200 when a rolling take off went awry because the Captain rushed the take off and flipped the Body Gear Steering toggle switch while the body gear was not yet neutral/centered. We lost traction on a just about wet RWY and thanks to providence, rotated to safety before reaching the RWY shoulder!
I feel distinctly uncomfortable if the Body Gear Steering is not available. It is probably one of the major reasons why the 747 is a great airplane to taxi. The 777 and 787 do not compare in the feelgood, feel comfortable sweepstakes, and I have extensive experience on all 3 types.
SO, to pique your interest in things similar, @No_Fly_Zone, the 777-300ER have something called "Semi-Levered-Gear" - go figure ...
