Burgers like any protein, your looking for a little char, to release the meat from the grill, give them a 45 turn, same time and flip them, 3 minutes on the first side means 3 minutes on the other side...the 45 turn us for presentation
I check for doneness with a thermometer or my thumb., and finish moving the meat to a cooler area of the grill, alway best to let it rest before serving...
Quail cooks very fast...a little oil will generate even faster heat..