Make Spotlight ignore external disks?

I have Time Machine backing up to four external disks, rotating one each week to another location.  But I have another where I manually run a script to back up a website and two specific large directory trees.  This disk will not eject, and gives no explanation when I try.  I suspect it is because as soon as it gets a new backup, Spotlight starts indexing it and 500GB takes a while. Unfortunately, in Sequoia 15.1.1 (24B91), external disks cannot be added to the Spotlight exclusion with the Settings GUI .  Clicking "+" does not allow navigating to them.  Drag-and-drop from Finder does nothing. defaults read com.apple.IMCoreSpotlight contains a key of IMCSDoNotIndex = ( ); but after I add two directories to the exclusions (with the Settings GUI), that key remains empty. If I read all nine domains associated with Spotlight, and search for those directories, neither is mentioned. **Is there another way to get an external disk excluded?**