If a critter uses binding on a target that doesn't have strength. What attribute should be rolled? For instance if it were used on a vehicle that is moving and the pilot of the vehicle "guns" the engine to attempt to get outta the bind.

I was thinking just using Body + Body, instead. Much like Jarheads use Body for Strength checks.

Any thoughts?

Without information about the vehicle's power source (its strength may be in horsepower), that seems to be the best that can be done.

Such things have object resistance depending on manufacturing complexity. If the mage overcomes that, there is no resistance roll.

One might have the pilot make a resistance roll, but that is GM fiat only.