disk not ejected properly when time machine runs

Hey there lth91,

Does changing the port the external drive is hooked up to have any impact on this? Test to verify as this can isolate the cause of this.

Another step that may help would be to run First Aid on the external drive. Here’s how:

1. Determine whether you're using a Mac with Apple silicon, then follow the appropriate steps:

* Apple silicon: Turn on your Mac and continue to press and hold the power button until you see the startup options window. Click the gear icon labeled Options, then click Continue.

* Intel processor: Turn on your Mac, then immediately press and hold these two keys until you see an Apple logo or other image: Command (⌘) and R.

4. You may be asked to select a user you know the password for. Select the user, then click Next and enter their administrator password.

5. From the utilities window in macOS Recovery, select Disk Utility and click Continue.

6.

Select your disk in Disk Utility

Choose View > Show All Devices (if available) from the menu bar or toolbar in Disk Utility.

The sidebar in Disk Utility should now show each available disk or other storage device, beginning with your startup disk. And beneath each disk you should see any containers and volumes on that disk. Don't see your disk?

In this example, the startup disk (APPLE SSD) has one container and two volumes (Macintosh HD, Macintosh HD - Data). Your disk might not have a container, and it might have a different number of volumes.

Repair volumes, then containers, then disks

For each disk that you're repairing, start by selecting the last volume on that disk, then click the First Aid button  or tab.

In this example, the last volume on the disk is Macintosh HD - Data.

Click Run to begin checking the selected volume for errors.

* If there is no Run button, click the Repair Disk button instead.

* If the button is dimmed and you can't click it, skip this step for the disk, container, or volume you selected.

* If you're asked for a password to unlock the disk, enter your administrator password.

After Disk Utility is done checking the volume, select the next item above it in the sidebar, then run First Aid again. Keep moving up the list, running First Aid for each volume on the disk, then each container on the disk, then finally the disk itself. 

The order of repair in this example was Macintosh HD - Data, then Macintosh HD, then Container disk4, then APPLE SSD.

When done, quit Disk Utility. If you used Disk Utility from macOS Recovery, you can now restart your Mac: choose Apple menu  > Restart.

You can read more here:

How to repair a Mac disk with Disk Utility 

Have a good day.