Wife and I shoot steel challenge and we've had one instructor refer to getting behind the gun. Now, I'm going to see him on Saturday and discuss, but I'd like to hear what others have to say.
Googling is useless - mostly rifle related and it seems a bit more literal as in get your weight behind the gun.
A Max Michel video talks about high grip and left hand cocked down at 45 degrees, but I don't believe that's the context to which I'm referring.
My own visualization, such as it is, is more akin to "getting ahead of the gun": process faster than I can manipulate the gun. Accelerate the gun, acquire the (next) target, decelerate, refine sight alignment picture, squeeze trigger. Ideally, some of this happens at a subconscious level, sight alignment is being refined during transitions, etc.
But if I can do anything else to "get behind the gun" I'm all over it.