Ok, I just did a proof of concept using a NodeMCU board and a BH1750 sensor. $20 for 2 of each on Amazon. I used a power supply I already had. It works great! The sensor is currently just taped to the top of Alexa so that lux is 0. The highest reading I have seen generated when she is talking is over 300 but it spends most of the time around 50. That's definitely high enough to use as a trigger.
Now to determine if the smaller lights on a Google Home Mini will work and to see if I can "borrow" an old radio from my dad.