Close Excel event to use with personal.xlsb file

I want to record the time I spend on Excel in my personal.xlsb file.
I have successfully used the Sub Workbook_Open event to write the start time, however I'm having difficulty finding an event to trigger writing the fnish time.

The Workbook_BeforeClose event does not seem to work when I close Excel. I was expecting the personal.xlsb file to be closed when I close Excel, but closing Excel does not trigger this event?

I can use the Workbook_BeforeSave event because the start time is being written and therefore the file has changed. However this means I'm always prompted to save the personal.xlsb file when exiting Excel. I prefer not to do this as its too easy to click "Don't Save", especially when a lot of other junk files are open.

Are there any other Event options I could use to trigger writing this finish time?

Maybe this Excel session time is already recorded somewhere else?

Yes I am doing a save within the close.
The problem is that the Close event does not seem to be triggered in the first place.

I'll check out Outlook journals.