Activity list is not showing emails in BusyContacts on macOS Catalina
macOS Catalina 10.15+ no longer provides email access to 3rd party apps.
Only Apple Mail on macOS 10.14 and below, and MailMate are supported. Apple has confirmed that macOS 10.15 Catalina no longer provides email access to 3rd party apps. If this bothers you, please leave Apple feedback, asking them to provide developers with such a feature.
There is unfortunately nothing that can be done about this till Apple provides developers with an ability to access this information.
If you're on macOS 10.14 or below and cannot see messages and/or emails, a Spotlight re-index may help.
BusyContacts uses macOS Spotlight to find and display your linked email/messages/etc. Here's how to reset this:
Open System Preferences
Click on Spotlight
Click on Search Results and in the list presented, make sure you have checked "Mail & Messages"
Click on the Privacy tab at the top and make sure ~/Library/Messages or ~/Library/Mail aren't excluded from Spotlight searches.
Next, try and rebuild your Spotlight index by doing the following:
Launch the Terminal.app (in /Applications/Utilities).
Paste the following two commands, pressing return after each:
mdimport -r /System/Library/Spotlight/Mail.mdimporter
mdimport -r /System/Library/Spotlight/Chat.mdimporter
Wait several minutes for the spotlight Mail index to be rebuilt.
If the above does not work, it may be worth rebuilding your entire Spotlight index. This can take several hours at times to finish in the background and you may not immediately see search results.
Please follow these instructions to rebuild the Spotlight index on your Mac.
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