That situation is one scenario where I turn the rear light on in daytime.
I find lights have about a 90% failure rate in a year. Rain has killed 3 LED versions, even inside the bag not in use. If not rain, battery leakage. If not that, battery contact corrosion. $60 for a piece of inert plastic offends my sensibilities. As most riders here don't ride in the rain, recommendations on the site don't sell me. I have a 18 months old $60 catseye light that rides in a peanut butter jar in the bag 99% of the time. The one time this summer I tried to use it, after dark, the battery went dead after 70 minutes. Rode to summer camp by starlight. I'm sorry, it takes me 255 minutes to finish my commute sometimes. What did work after dark, my ANSI class 2 construction vest, which is highly reflective in headlights of cars.
Buying a $2500 ebike with integrated lights and a display that fails in the rain is another sales pitch that doesn't move my debit card. My bike has no display.
One taillight that works in the rain and has been good for 3 years, is the Garmin Varia radar motion detector. As a hazard warning device it is a complete failure. Wolf! wolf! wolf! wolf! wolf! wolf! wolf! As a tailight it has been very reliable, at a cost of $240. On flash battery lasts about 6 hours. I do have a plastic rainshield over it. No easy way to build one of those over a light that clips to the handlebar.