That is really odd. The best thing to do with something like this is to start checking connections and grounds. Something could be loose or corroded.
I do have a question. If the engine is warm and you start the engine first, does the same thing happen? Also, here is a link you may find helpful:
I attached the wiring schematic for the headlamp system. I had to cut the pic in half to make it readable, but I did overlap them so you can easily follow. Check the connectors at the headlamps, the grounds, and make sure fuses are not corroded.
Let me know what you find.
Images (Click to enlarge)
Monday, April 5th, 2021 AT 6:29 PM