I don't know about Coturnix, but button quail I do. They stay skittish. They often jump high and bump their heads on the ceiling of the enclosure. When they jump up, they can go almost 5 feet up. Had one break her neck doing that. They also can jump at the angle of your arm to gain freedom when you are changing out the water and adding feed . Cleaning the enclosure requires I remove the button quail- stressful for us both. I have had one or two get away from me and then had to go on a treasure hunt- they can hide in small places and even get under doors if there is a gap. I don't recommend them for casual pet owners. They are cute and I love the way each enclosure calls to the others, but it does take some time and energy to care for them.
^^^ this! no matter how we raised the different batches of buttons we had, they stay skittish. We had ONE exception, Link was very friendly and loved to be out but not held, he'd just sit next to my computer or on the arm of my chair to just 'hang out' but not really be held, snuggled or anything. He was a really cool companion, a really good dad too but even the chicks he hatched turned super skittish. I know some people have friendly buttons but I've never experienced had that :')