A=U F2 U' F2 U'
B=R2
A'=U F2 U F2 U'
B'=R2
[thread hijack]
That is my favorite commutator out of all of the corner ones. The A part is really beautiful once you understand what it's effect is and how it achieves it.
[/thread hijack]
like say you had a commutator where you had 2 stickers on the U layer facing up and the lone corner in the D layer facing down. When you "see" this you know that it is not the simple commutator and needs 12 moves to be solved...
Not all cases of that type need 12 moves.
case 1) UBL -> DLB -> URB: D L2 D R2 D' L2 D R2 D2
case 2) UBL -> DLB -> URF: R' U2 R U L2 U' R' U L2 U R
I do agree though that you learn to see, based on how the stickers are situated in relation to eachother, which case type you have. It's a lot like F2L in CFOP solving actually. You could memorize every possible case as an "algorithm" or learn a small group of types of commutators and learn how to recognize them on other faces or from different angles. That's all BH is really. As for R2 commutators, try looking at the BH corner commutators first to see if you find one you like. If those don't work, or you don't like them, then try freestlye using setups and A perms or setting up into one of a couple simple commutators that you can recognize easily.
Hope that helps at least a bit,
Chris