Can't access hard drive backups in Time Machine

Update.....I ran a test by using a WiFi connection from my Mac to the Time Capsule. I waited for about 10 minutes for Time Machine to load.

The external drive was not connected to the Mac at all. it was powered off.

Using the steps that I provided above, Time Machine allowed allowed me to "see" the external drive, and I could easily view the contents of the drive as well.

The tricky part is right-clicking to select a file or folder (or the entire hard drive) to bring up the "Restore To" options to restore the selected data to a destination of your choice. This could be another hard drive connected to the Mac, or you could restore the contents of the external drive to the desktop on the Mac.

You are not doing anything wrong......except maybe not looking in the right place.

Keep the external drive powered off

Open up Time Machine and give it 3-4 minutes to fully load

Go back a few days in time using the scale on the right side of the window

Look on the left panel or side of the Time Machine Finder window and look for the name of your Mac under the Devices heading

Click on your Mac under Devices and then look in the window to the right and you will see two folders...... Macintosh HD (unless you have changed it to another name) and the name of the external hard drive

Right-click on the hard drive and you will see that you have options to Restore the data on the external drive to another location.....so you can restore the contents of the external drive to another drive.....or to the desktop on your Mac if you want

It will work if the data on the external drive really has been being backed up along with your Mac.

But....and this confuses a number of users.....the external is not going to be backed up along with your Mac......unless.....you have removed it from the list of Excluded Items in Time Machine Preferences / Options.

You did not mention in your post whether or not you had already done this.

In other words, the external drive is excluded from being backed up as a default setting in Time Machine. Simply connecting the drive to your Mac will not enable Time Machine backups of the external drive. So, the external is not being backed up unless you have made the appropriate changes to allow this to occur.

If you are using wireless on your Mac to access the backups on the Time Capsule, it may take some time for things to fully load. Allow 10-15 minutes at least.

Would be much better if you could connect your Mac to the Time Capsule using an Ethernet cable and turn off the WiFi on the Mac.