Quail are very seasonal layers. Ours usually stop laying in mid- late September and start again at Easer time.
As you say, it is due to day length and temperature. Guessing that if you wanted to keep them in lay you would need artificial lighting .... as some people use to keep hens in lay. I just let mine have their rest.
This year for us has been a little different. Ours continued to lay into November and started again a couple of weeks ago! Assuming due to a very mild autumn and December and assuming they will now stop again now as it has just started to snow!