I think I finally understand this.
As I noted earlier, they were doing some rewiring of the apartment complex when I encountered this. Shortly thereafter I also started having problems with a Tripp-Lite UPS which had been trouble free for 5+ years. About once each day and always in the morning, the UPS would briefly interrupt power to my main PC (on the same breaker as the chandelier). I assumed this was also connected to the wiring changes since it started at about the same time. The UPS has 6 power protected outlets and 6 surge protected outlets. I plugged a low wattage lamp into a surge protected outlet and waited for the next power interruption. When it came and did not affect the lamp it was apparent that the the UPS was faulty.
I replaced the UPS a week ago and there have been no power interruptions since. And, when I tried an LED in the affected chandelier, the faint glow (and the 10V) when off is now gone. I think the UPS was spewing some high frequency noise.