True ambidexterity is not the great ability many people seem to think it is. We have a daughter who is a rare, truly ambidextrous person. She was diagnosed about 10 years ago. Hokkmike hit the nail right on the head - our daughter, who's 29 now, exhibits every one of those 7 characteristics Hokkmike listed, plus a few more.
We were always kind of proud of the fact that, among other abilities, as our daughter was growing up and doing her homework at the kitchen table, when whichever hand she was writing with got tired, she simply switched her pencil to the other hand and kept going. We joked about her not knowing her right from her left. But the jokes ended when we found out she couldn't tell time except on a digital clock and she was nearly 20 years old. "Clockwise" simply doesn't mean a thing to our daughter. To her, it makes just as much sense that the hands on a clock turn to the left as to the right. Oh yeah, she could read a clock if it was on the hour, or even the half hour and the clock had real numbers on its face, but if was 10 minutes after, or 10 minutes before the hour, forget it, because our daughter didn't know which way the hands on the clock were moving. Through will power she still tries to overcome that little disability - she refuses to wear a digital watch. But if you ask her the time, even today, it takes her a few seconds to respond because she has to observe which way the second hand on her watch is moving.
Oh, and tightening a screw or a nut, taking the lid off a jar, closing a valve and all of the other little things that most people do everyday without thinking, present challanges to the truly ambidextous person. Great ability indeed!
I'll tell you all another thing too - You never want to get directions from a truly ambidextrous person unless you understand the way they think. After our daughter graduated from college (with high honors I might add) she spent a couple of summers working summer theater up in Big Fork, Montana. When we went up to visit her once, I asked for directions to her place. She told me to go to the "big bear statue in the middle of town and turn." Then she said "go to the school and turn again. My place will be up the hill at the end of the road." I knew better than to ask which direction to "turn." She just didn't know. So when we got to Big Fork, we figured it out - if we'd have turned left at the "bear statue" we'd have gone into the lake. And we had to turn left at the school to go "up the hill."
Our daughter has a great attitude about her disability though. A few years ago my wife sent her one of those stupid "find your soulmate" surveys out of a women's magazine and one of the questions was; "Which hand do you use when you're brushing your hair?' Our daughter responded with; "I don't know, but I can brush my teeth or put on my makeup at the same time!"
Just to keep this gun related - we taught our daughter to shoot right handed because most guns are built for right handed people. Besides, my wife and I are both right handed so we didn't have any left handed guns to teach with.