Time Machine discs generally won't reach "full." When the disc runs out of room, TM starts deleting the older copies of files that are backed up to replace them with newer versions (this is- in effect- cutting how far "back in time" you can go if you want to retrieve an older version(s) of some file). So it should never run out of room assuming the TM disc is bigger than the Mac disc(s) to be backed up (ideally at least 3X-4X bigger or more). There are occasionally posts about people's TM disc reporting "full." If yours is, you might reformat it to blank and make it a fresh TM backup again. Again, "full" should not occur when everything is working right and you have abundant TM space (bigger than the Mac(s) to be backed up... ideally much bigger).
Assuming your TM disc is still attached to the Mac you want to back up, maybe the enclosure needs to be rebooted?
Are enclosure indicator lights on and everything looks right? Maybe the enclosure is dead? Do you see the TM disc as available to you in Finder, which will show you it is still connected? If you click on that disc in Finder, will it open so you know the drive is accessible?
Is TM app turned on in Apple (icon menu), System Settings, General tab, Time Machine? Do you see your TM disc at the top? Does "Backups" show
today's date and up to about an hour ago or something else?
If you see no disc there, click the + button and then select your TM disc to show Mac where you want TM to store its backups. It may want to make a fresh backup and- depending on how much you have on your Mac- that can take many hours the first time. Just let it do it (perhaps while you sleep overnight). Subsequent (and automatic) backups on the hour should be very quick.
You probably have a TM icon up in the upper right menu bar. It looks like the hands of a clock with a counter-clockwise-pointing arrow around it. If so, click on that. The menu that opens should show some information about last backup and an option to "Back Up Now." Try clicking that option and then see what happens. It will either start backing up now or prompt you regarding why it can't.
TM backs up just about everything. Some things that can be downloaded from Apple's servers aren't backed up but drawn from Apple in a "restore everything" scenario such as a dead/stolen Mac getting replaced. But your own creations/data should be backed up in TM (as Apple wouldn't be storing any of that).
CCC is an alternative to TM. I believe it too can be set to
do automatic backups like TM. Many people like to use
both:
- TM auto-backups to one disk
- CCC (or SuperDuper) to another disk
It is a very good idea to have at least TWO backups of your Mac(s), ideally with one stored
offsite such as in a bank safe deposit box. The offsite one should be regularly rotated with the onsite backup disc so that BOTH are pretty fresh backups. This strategy protects against very real threats like fire/flood/theft where BOTH Mac and the TM/CCC backup at home are lost. That offsite recently-up-to-date copy then "saves" you.
Key here is regular rotation so that your latest new files are on that offsite backup.
For example, if you delay this rotation 6 months and there is a fire/flood/theft, you lose up to the last 6 months of new files/data in a restore from the offsite backup. On the other hand, if you rotate the 2 backup disks- say- monthly, your worst case scenario is losing up to the last 30 days or so of newest files/data.
I hope this is helpful to get your data protected again. I strongly suggest you heed that (at least) 2 backups tip too. The most common ways data is lost for many are ways that take out your Mac and a TM disc right next to it at the
same time. As little as just ONE+ offsite
fresh backup will save that terrible day. And gigantic HDD storage is dirt cheap.
