Spotlight won't search my external drive

I've followed instructions from previous posts about how to re-build Spotlight after updating to Catalina. Data stored on internal drive shows up in Spotlight but not on external drive. When I try to drag it to the Privacy window in Spotlight Preferences, I get the message "___ is a Time Machine Back-Up folder. You cannot add it to the privacy list."

That's not the only reason I use that drive, so I need to be able to search for items on it. Here's what I've tried so far:

1.  Dragging individual folders that I need indexed within the external drive. (Same error message)

2.  Removing that external drive from Time Machine Back-up, followed by a restart (same error message)