I find it depends heavily on the "type" of rain. Not very scientific here, but smaller more misty drops won't trigger it, but a downpour with lots of water that runs down the windshield seems to trigger it more often. I think it has to do with the water running down the windshield, maybe it's movement based.
I would agree with that assessment as well. Type of rain, and time of day (and firmware version) all seem to play a part. When I first got my car it was december of 2018, and california doesnt have true winter, but we do get rain in the winter. We got a fair amount (for california) of rain between december and, say march / april, and the "auto" wipers were so bad I told my wife I didnt want her driving the tesla at all.
Its my primary car, but we switch off driving each others cars normally just for changes of pace. I had to use the manual wipe almost constantly while driving. Setting it to a speed resulted in either too fast, or too slow, and auto didnt wipe enough so I had to supplement it with pushing the button at the end of the stalk. Coming from my BMW (and my wifes existing one) where the feature "just works" and always seems to wipe as expected, it was upsetting to have the tesla always wait too long to wipe.
Sometime during the above period, it got "better", with better defined as "almost tolerable". Then, we got out of the rainy season so I have not seen its operation over the past few months. I am dreading fall actually because as I mentioned, the auto wiper lack of consistent operation is really my biggest complaint with the car. Even when I mentioned " fit and finish" above, that was in relation to the paint job on my former and wifes current BMW. the BMW is just put together better imho, but my tesla is "fine" and is so much better to actually drive that I have no issue overlooking the small fit / finish issues I have on my car.