Yeah… if you can’t keep your balance, you probably need to think hard before trying the “riding in traffic” thing anyway. 
It’s easy. Don’t lean over too far.
I used to use them when I road a motor cycle, if my signals were out.
I don’t think I’ve ever seen another driver do this, nor did I learn it. But I’ve definitely seen cyclists (bicycle, not motorcycle riders) do it.
BTW a belated thanks for all the replies.
Around here I mostly see biker chicks on the back of Harleys using the hand signals. They are pretty diligent, like they are in charge of *all *hand signaling on this machine, Dammit! Sometimes it’s on a chopper with the electric signals removed in the interest of coolness but often hand signaling is in addition to the electric signals.
I’ve also seen them extend the left arm at about 45 degrees (down) and the index finger pointing at the ground with an up and down motion of the whole arm indicating “slow down.”
I’m not sure how “official” that last one is but I’ve seen it quite a few times, mostly when the bikes are in a group and the slow down signal seems directed at the riders behind them.
Descriptions of hand signals, including the signal for stop (left or right hand downward), is listed in the South Carolina Driver Manual under “Sharing the Road with Cyclists”.