Kappy, I appreciate your advice but I did all of that and it still auto-restarts. Reset SMC, NVRAM, SRAM, restarted in Recovery, used Disc Utility First Aid in Recovery. Yesterday took hours (used 2nd security option of 2 rewrites) to erase HD and reinstall OSX all from recovery. Then of course got update notification so updates with recent Supplemental. Nothing changed. I think this has got to be a problem with High Sierra. I've had this issue since 1st High Sierra installation months ago.
**Previous to erase/reinstall, when I started in Safe Mode got a lot of flickering on monitor and slower response on everything. Some programs are disabled by design. BUT, it DID NOT RESTART during a roughly 24 hour test period. Normally restarts randomly within minutes to hours. I don't know what this means or how this can help. Any thoughts?
late 2012 iMac 21"