Because of the postings on this discussion I was able to do this.
At the risk of being repetitive this is what happened to me.
I wanted to use a new external drive for my Time Machine backups.
When I unlocked the "Get Info" Window on the newly formated drive
then the option to [Ignore ownership on this volume] was displayed at bottom of Get Info Window
The box could be checked and unchecked.
While the box was unchecked I copied all my previous Time Machine Backup Files from the old drive to the new drive. Still the "Ignore ownership..." box could be checked and unchecked. I left it unchecked.
Then in Time Machine Preferences I selected the new drive as a backup disk.
After that I wanted to see if the box could be selected and unselected as before. But when I checked the box for [Ignore ownership on this volume], the box and text disappeared.
The old external drive that was previously used for backups was not displaying "Ignore ownership..."
After I erased the old drive [Ignore ownership on this volume] was displayed on the "Get Info" window after I clicked the lock and unlocked it. Then on the old drive "Ignore ownership..." could be selected and unselected.