Thought I might take a "swing" at "muscle memory"....it isn't.
The reference, though common and incorrectly named does refer to a learning process. I learned to call it "establishing a motor program".
What we're doing with high rep training is executing the same series of movements in a fixed pattern until such time as we no longer need to devote primary thought processes to executing them. Learning to walk is a great example (though most of us here learned to do it long enough in the past that we likely don't remember the learning process.) We no longer give a great deal of thought to walking other than "go" or "stop". However, if you take a careful look at all the movements and shifts in balance required to take one step, you'll find that it's not a simple process at all. The reason we don't seem to do the "calculations" in our heads every time we take a step, is that we've done 'em so much that walking has it's own "sub-routine" that we "run" in the background.
The same thing applies to carrying/drawing a sidearm and performing the "chores" that keep that piece of equipment operating. You establish a "motor program" for your draw, and it gets accessed by (for instance) an audible signal like gunfire (or the words "stick 'em up" or perhaps the beep from a pac timer), or maybe you see something "bad".....you won't think about exactly where the weapon is on your person, it'll seemingly "appear" in your hand...you may not even remember reaching for it, or making a decision to do so.
I was practicing on a range a few months ago and had failed to shift my phone away from the mag pouch when setting up....I went to reload and had the phone firmly indexed into the butt of the pistol before I realized it wasn't a magazine....
Motor Programs.....ask for 'em by name.
In answer to the OP's question....strong side hip or I'll use a "fanny pack" (Found one that doesn't say "Hey, I'm carrying"). My motor programs are MUCH better for hip, but getting pretty good with the pack also.
