How do I update my Mac OS to 10.12 if it is not appearing on 'updates'

The move from El Capitan (10.11) to Sierra (10.12) is not an update, but rather a full upgrade, and that will not appear in your El Capitan Mac App Store Updates panel. You would have to obtain the full installer from the Mac App Store.

If your Mac can run Sierra (10.12), it can run High Sierra (10.13), and the Mac App Store will know this and likely block the download of Sierra. With the release of macOS Catalina, Sierra also falls of the normal three year operating system support cycle, which you would be covered with High Sierra.

Check the parenthesis contents in your Mac description line of the menu : About This Mac. If what is in the parenthesis, agrees with the hardware requirements for upgrading to High Sierra, then you can download High Sierra from that article which has a link to it in the Mac App Store.

Before any upgrade, run a final Time Machine backup. Perhaps even clone your boot drive to an external drive using Carbon Copy Cloner, or SuperDuper!. Check that your printer and scanner drivers have been kept current by the respective product vendor, and that there are no limitations with third-party installed software lacking support on High Sierra. Do not reuse your El Capitan Time Machine drive on High Sierra, as it is your get out of jail free card if you want to restore from it back to El Capitan.