LED light with built-in switch; installing auto-timer between switch & outlet,
Into the trash it goes

The timer is almost certainly malfunctioning and not providing "clean" voltage &amp; current to the lighting. 

This surely has something to do with "leakage current" as we often see with devices working fine with incandescent and then choking on LED.  However there's no reason for a timer to be built that way.  Further, the fact that it started doing this now proves it's some sort of electronic degradation. 

Look at the timer; if "CE" (Chinese Excrement) is the most prominent listing agency mark, then waste no further time on it.  Amazon Marketplace, eBay or Aliwhatever are not reliable sources for quality parts.