Okay thanks for the replies.
10.15.5 on a Late 2014 Retina 5K iMac. The external hard drive is brand new, 32 days old.
I know its Spotlight because I can hear it when Spotlight is enabled for the drive, and goes away when I add the external HDD to the Privacy tab of Spotlight in System Prefernces.
Maybe erasing/rebuilding Spotlight index with terminal commands is the way to go. Shrug
Thanks again for the help and please excuse any snark on my side.