Please don't make multiple posts. It isn't necessary if you choose the proper forum.
Open the Terminal in the Utilities folder and enter or paste the appropriate command line. Press RETURN and enter your admin password when prompted. It will not be echoed.
To turn them ON: sudo tmutil enablelocal
To turn them OFF: sudo tmutil disablelocal
Note that turning them OFF will also delete all existing snapshots.
I'm sorry but I didn't find a post that I found helped to the point of resolving my 'issue'.
As for the items that are marked as other, is there a way to figure out what they are? It was at 0KB before I deleted the backups and now it is at 27GB.
Is the main drawback of stopping these 'local' backups that my computer will only have backups as resent as my last backup onto my external hard drive? Or are there other functions that are affected?
First, be sure to only use the command that turns SnapShots OFF. Stopping local snapshots will prevent Time Machine from creating backups on your computer instead of on your backup drive. Or turn off Time Machine backup in the Time Machine preference pane.