Think about something simple you do all the time, out of habit. Does it require lots of energy or strain? Could you think of a way to do it "better" than how your body has naturally done it unconsciously for years?
For example, say you're standing and I ask you in which direction the bathroom is. I bet you'd gently raise whichever arm is closest to the direction you wish to point, and your entire body would adjust slightly to make your arm point in the correct direction with maximal skeletal support and minimal muscular effort. If someone happened to be standing in the path of your pointing arm and you were not aware of this, s/he would likely get a hefty whack or poke, due to your natural looseness and body unity. You would NOT keep your body stone still and strain to contort your far arm across your body to point in the right direction. That would look weird and would not be comfortable.
Likewise, when you do something mundane with your hands, say preparing breakfast, you naturally do it within your "work space" and move efficiently to bring things into your work space. As you prepare your breakfast, you'll use both hands in coordination at a comfortable distance in front of you to get things done with minimal effort. If you need to reach for an ingredient or utensil to your right, you probably won't use your left hand to reach for it. You'll use your right hand, and your whole body will shift to minimize the amount of "reach" and effort your right arm must exert. To do otherwise would feel weird.
When you're practicing contact flow, move your body such that your left hand stays on your left side, your right hand stays on your right side, and the action remains mostly within your natural work space. If your training partner tries to push your hands out to your right, shift and turn your body such that you keep your hands in front of you, neither hand crossing over your center to where it doesn't belong. If your training partner tries to cross your hands over each other, move your body such that they don't cross. Incidentally, if you've worked with Lt. Col. Al, you've probably had the experience of getting your arms crossed over each other and tied up while he strikes. Most likely, you actually caused that to happen yourself, by reaching across your own body unnaturally rather than moving your body to keep things as they should be. Al is just VERY good at taking advantage of that (as are all the GC masters--they just tend to capitalize on different mistakes given their natural proclivities and your bad habits).
Think about it: If both of your arms are on one side of your body, how can you protect the other side, against your current training partner or another who might suddenly attack you? This applies even when striking with your elbows. If your elbow is up to strike in some kind of horizontal slashing or thrusting motion, make sure the hand attached to that arm does not collapse past your center to the other side of your body. All that does is wrap your arm around yourself in a constricted and vulnerable way, reducing your elbow's reach and skeletal support and tying yourself up, "gift-wrapping" you for the enemy. If that arm is under pressure, move your body to nullify that pressure rather than allowing your arm to collapse into an unnatural position.
Incidentally, in contact flow, if you are not close enough to actually hit with your elbow, it should hang loosely from your shoulder, pointed towards the ground, rather than flapping in the air like a chicken wing, adding unnecessary tension to your shoulder and exposing your body to attack, as well as setting itself up for locks and breaks.
Please do not interpret any of the above as absolute "rules" ("Never let your hand cross center! Elbows should always be DOWN!"). They are general guidelines to improve your body unity, efficiency and natural movement in contact flow. Note that you do NOT keep your hands in better position via force or resistance. Instead, you move your body appropriately to keep it in better position relative to your hands. This body movement comes from the legs, not from the waist or shoulders. Your training partner can push your hands wherever s/he wants to. It doesn't matter, as your body will naturally move to keep your hands and arms in natural, comfortable positions relative to your body. And you'll see that the better this happens, the more your training partner will "accidentally" run into dangerous parts of your skeleton (striking ridges like palms, edges of hands and elbows), fully supported by your loose, unitized motion.