I contacted support and after 4 hours of 'problem isolation' they asked me to re arrange all my cameras on different bases to see if I still had the problem. No thanks. I will just add it to my list of idiosyncrasies with Arlo, and move on.
Arlo is complex. Cameras, hubs, apps on various platforms, servers, internet connections, etc. and then constantly introducing new hardware and new features. It is a marvel that it works at all.
I opened a case for this problem, 41363583. I also added a second rule on the light to trigger a recording on a different Pro 3 camera on a different hub. The problem is the same ie it records to the cloud, but not locally. So this occurs on both the VMB5000 and the VMB4540.
I also have the problem reported elsewhere, that sporadically I get a recording locally that does not make it to the cloud. This has nothing to do with the light.
I also notice that if the camera you want to trigger does not have an active rule, ie it is not detecting motion, the light will not trigger it at all. Not sure if this is by design or not, but useful to know if you are wanting video