Okay, I will have to "Put my foot down" on this one. Always, always, always... Both for me. Or one if I run out of "always's". (Like a stop and go cause the light just turned green) .. Or if you are real good "none".. However If a guy says none.. You can spot his bike in a crowd.. It has all the scratches and duct tape on it... Not that mine is perfect either, but not from dumping it because I didn't put my foot (feet) down. More like curb rubs and garage dings.
Enough nonsense... Use your best judgement. If both feet can reach the ground and you are asking this question, you are probably a beginning rider.. And you might be advised to use both in this case. Naturally if both will not reach the pavement scooch your butt left or right, tweak your cheeks and try to get one tippy toe in contact with the pavement. No fair using the curb.. Sometimes they will not be there. If your feel (foot) cannot reach the ground, perhaps a smaller scooter is what you need.
The above answers are probably not what you are looking for, but the important thing is that you stop at intersections and look both ways while in full control of your scooter. If you cannot balance your scooter, then by all means stop it and let it fall. Better that than to suffer the consequences.