What muscles am I using when wheeling?
Wheelies aren't a strength thing, they are a function of weight distribution on the bike.

If you move your weight far enough back the front wheel will lift - this can initially be assisted by applying a few hard pedal strokes in a light gear.  As you correctly observed, rear suspension is a disadvantage here, as it absorbs some of your initial weight movement.
Once the front wheel is up its about maintaining your balance point.

As with anything balance related, some core strength conditioning will help, but is not really much of a determining factor in ability to wheelie for long durations.