Hi,
I agree with what everyone has been telling you. For quail to lay eggs there is a combination of 3 elements that have to come together.
1. Proper diet.
2. Amount of light.
3. Temperature.
This is what works for me. Have the birds on a layer diet, this way they are provided the proper amount of nutrients, vitamins and protein.
If natural light is available in you garage, provide as much of that as possible. For using artificial lighting, fluorescent bulbs seem to work best for me and they use less electricity. I know that 14 hours of light should be enough but 16 hours does the job for my birds.
My quail seem to respond well to 60 F degrees.
I definitely agree with Joe on adding more females to help justify cost. The coturnix quail you have are 3.5 months old and if you can't get them laying now, by next Spring they will already have surpassed their peak laying age.
The pecking would indicate some kind of stress. That definitely has to be dealt with, you only have 2 in the cage so overcrowding is not an issue. I think you said that you have some buttons in a cage right next to them. So what would make the least amount of sense that would be causing the stress. Can your Coturnix actually see your buttons? That certainly shouldn't matter should it. So if they can see the buttons, I think that I would start by blocking their view of them. Second, they are definitely not overcrowded so I take some string and a couple old CD's and tie the string to the top of the cage and the other end to the CD and let the hang down in several areas of the cage. This will give them something else to peck on instead of each other.
I don't know if anything I have mentioned will help your situation, but they do work for me.
Good Luck