The iCloud Photo Library is a syncing service, not a back up.
Putting the Macs Photos Library on any sort of Cloud service is not supported. If you do it it will be corrupted and cause dataloss. (There's a handy definition of ineligible for you there :) )
To back up the Photos Library:
Most Simple Back Up:
Drag the Photos Library from your Pictures Folder (or wherever you store it) to another Disk. This will make a copy on that disk.
Slightly more complex:
Use an app that will do incremental back ups. This is a very good way to work. The first time you run the back up the app will make a complete copy of the Library. Thereafter it will update the back up with the changes you have made. That makes subsequent back ups much faster. Many of these apps also have scheduling capabilities: So set it up and it will do the back up automatically.
Example of such apps: Chronosync, SuperDuper, Carbon Copy Cloner - but there are many others. Search on MacUpdate or the App Store