I found found the problem! It was the <i>CrxMouse Chrome™ Gestures</i> Chrome extension. I will report this to the extension author.
I’m beginning to suspect this might be something in my Chrome browser setup. I am seeing the error on this forum Web site too! But not in Edge. I’m investigating further…
As I mentioned, this is a 100% clean install of WordPress (WAMP Win10, but I also see the exact same 404 error on Pantheon, MediaTemple, Bluehost installs).
Something in the core install is looking for /null on every page request. I have no idea what it is or if there’s a basic setting I’m missing.. If you want a see it in action, open the Web Dev console on these sites (all on different hosts):
http://robertgomez.org/
https://sabrahealth.com/
https://incohoat.com/
I have re-saved permalinks on all these sites and the error persists, even for anonymous users.