Well, that was silly. I didn't pay close attention to this before, but what I have been calling "lux" throughout is not lux at all. It's still a useful value (for this scenario), but it's just not lux.

ESPHome supports the obsolete TSL2561 device but not the replacement TSL2591 device. Over the last few days, I undertook adding support for the TSL2591 device to ESPHome. (Here are the pull requests, if you are interested: https://github.com/esphome/esphome/pull/2131, https://github.com/esphome/esphome-docs/pull/1370). It was only while working through the details of that that I started paying more attention to what I was measuring.

What I have been calling "lux" is actually just the raw value of a 16 bit ADC for one of the sensors on the device. To get actual lux values, you have to do a calculation based on the ADC readings of both sensors. The calculation involves the configured gain, the configured integration time, and some empirically-determined coefficients. It is fairly complicated and scenario-specific to tune the calculation, but there is a calculation implemented in the Adafruit TSL2591 library. (Actually, there are 3 different calculations there, but 2 of them are commented out.)

In my ESPHome integration, I decided to make the raw ADC values available in addition to the calculation provided by the Adafruit library. That way, anyone who wanted to do their own calculation would have the inputs they needed (well, they also need a handful of physical characteristics that are out of scope for how much work I am willing to do for my own feeble efforts).

What does this mean for this project? Not much, in practice. I'm going to continue using that raw ADC read-out ("full_spectrum" in the graphic below), even given my better understanding of what it is, because it suits the coarse-grained conditional logic needed here.

I did not have an intuitive feel for real world lux values (like I do for furlongs, fortnights, and shillings and pence) until I looked at the Wikipedia article about lux. It has a nice table of a few examples. It tells me that what I see when the pilot light is on the order magnitude of some kind of moonlight on a clear night. Fair enough.

Here are some sensor readings that show the ADC values (600ms integration time, 428x gain) as well as the lux calculation from the Adafruit library: