Windows Backup is backing up an external drive as well as my C drive

Windows Backup works in mysterious ways.

That's one of the reason many avoid it. It's not intuitive or easily understood.

It has it's own idea of what needs to be backed up.

Post a screen shot of Windows Disk Management.

I don't see anything in that pic that would explain why F is included.

If you were using another imaging app such as Macrium, you'd only have to back up System Reserved and C.

As far as I can see from your pic, that's all Windows Backup would insist on as well.

So---my best guess is that you have made a mistake in configuring Windows Backup to do the job----checked a box you shouldn't have, not checked a box you should have---that type of thing.

But as I said---it's cryptic and confusing. I tried it once 6 or 8 years ago and quit it immediately. I saw no reason to attempt to understand it when there were simpler alternatives. So I can't help further.

Other members acknowledge that it's very testy but OK once you understand it fully. Maybe they will chime in.

The favorite on this forum is probably Macrium Reflect Free Edition. Simple understandable interface. 5 or 6 clicks to make an image once you install it.

Macrium Reflect Free

There is a paid version, but you shouldn't need it.

Others to consider: Acronis, Aomei Backupper, and Easeus Todo Backup.

You'd need to make a "recovery" disk or USB stick from within Macrium in order to restore an image. Without it, you're dead in the water. Confirm it will boot your PC. I just burn a CD following Macrium's instructions. You can burn a "Win PE" disk or a "Linux-based" disc from the menu. Choose the Win PE method--it's less prone to problems. Regardless, you need to confirm this burned disc will in fact boot your PC. If it doesn't, start a thread about that problem.

Reliability with Macrium probably 98 plus percent.

When you go to make your image, I'd just make a single image file containing both C and System Reserved as shown in your screen shot. You could make separate images of each, but there's no particular advantage to doing that.

This image file will have an mrimg extension and will be roughly half the size of the occupied space on C.

You can store that file anywhere it will fit other than C.

Just make a new one periodically--weekly, monthly, whatever suits you.

The image file will contain EVERYTHING on C, but images aren't really the best method of backing up personal data if you happen to have any of that on C.

"...If you were using another imaging app such as Macrium, you'd only have to back up System Reserved and C. ..."
"...Macrium Reflect Free -- There is a paid version, but you shouldn't need it..." -- ignatzatsonic

Within Macrium's image backup menu [somewhere], sometimes one has to UNcheck several boxes because all discovered partitions Macrium believes can be backed. Watch for those checked boxes!
And, if one is not used to making WinPE or Rufus USB or DVD boots, Macrium Reflect Pro has an EZ usb or dvd boot maker. Now, the only problem with that EZ maker: sometimes getting connected to a Macrium server for a much-needed download is difficult. End-user has no control over this, end-user can only wait, hope, and quoting Day After Tomorrow: "...pray."
Other than that, Macrium Reflect is one of the best ways to go. I also use Acronis True Image for "double backups."