Trying to allow my Airport backup through time machine to include my attached G Drive Mobile when backups are run. Shows the drive in history but can not click it open

I assume that you are backing up to a Time Capsule, correct?

Disconnect the G Drive from your Mac to simulate a situation where the drive has failed, and you need to get at the data on the drive on your Time Machine Backup.

Open Time Machine on your Mac and give it a few minutes to fully load

Using the timeline on the right of Time Machine window, go back a few days in the past to select a date

Look on the left side of the Finder window in Time Machine for a heading called Devices

Click on the name of your Mac computer under the Devices heading

The window to the right should display two folders, each representing a hard drive that has been backed up

The backups of your Mac are in a folder called Data.....(unless you have changed the name of the drive on the Time Capsule)

The other folder should display the name of the G Drive

Right-Click on the G Drive and a drop down menu will appear

Click Restore To to select a destination where the entire backup of the G Drive will go

If you don't want to restore the entire G Drive, open up the drive in Time Machine and navigate to find the file or folders that you need

Then, click to select and highlight the folder(s) and then Right-Click to display the Restore To option

You don't mention whether you have already checked to make sure that the steps below have been performed, but if they have not, they will need to be done before Time Machine will be able to back up the G Drive

1) The G Drive must be formatted in Mac OS Extended (Journaled) to allow Time Machine to back up the data on the Mac.

2) The G Drive will by default be excluded from Time Machine backups, so you must remove it from the list of Excluded items in Time Machine Preferences / Options before the drive will be backed up.

I don't have a G Drive here to test, but I have no problems with Time Machine backups of an attached Lacie drive, and a WD Passport drive.

Perhaps another G Drive user will post to help us out.

Did you ask G Drive Support about this? They should be aware of any issues that have been reported by other G Drive users.

I assume that the drive is connected to your computer using USB, correct? If it is, you will see the drive's icon on the Mac desktop.

Right-Click not the drive's icon and then choose Get Info

Look for Format in the window that appears with info about the drive