I figured something like that. I should have taken the shot when I was younger and more profitable. There's always the lottery.
You should stop calling them dumb questions. They aren't. In fact, your 'dumb questions" lead to a lot of new information even for me. I may be an entomologist, but that only includes knowledge of a fraction of the insect world and their varied lives. Ants and termites, unfortunately, are not groups I know a great deal about beyond the general. But the leg up I have may be enough to point us in a direction.
These flights are called nuptial flights and the winged drones and virgin queens are referred to as alates. Knowing those terms seems to be the leg up. I found these searching using those terms and hopefully you will find it useful.
Flying ant day: when winged ants take their nuptial flight
Nuptial Flights and Mating - AntWiki
The latter, I think will be more useful in answering your questions regarding timing. Search the text using this quoted passage as a guide.
"Queens of at least two species, Pogonomyrmex californicus and Mesor (= Veromessor) pergandei, also display circadian rhythms, and these are more or less synchronous with those of the males (McCluskey, 1967; McCluskey and Carter, 1969)."
At this point in the text it proceeds to discuss the species specificity of timing and confirms you observation about rain and provides more detail.
Both are pretty good sources, but the first is a general public version and the latter is more in depth.
I would probably have a tough time in my initial attempts at ID without the wings. I would hope that I could figure it out pretty quickly under closer examination given that the stumps of the wings are usually present.