Unfortunately, no, this does not help. I need to know how to trigger this automatically and the docs do not mention anything about that.
When I click that button, what action/hook is firing and can I trigger it on my own automatically without having to manually click it?
"If there are too many, Toolset will start a cron job. "
What is the name of the job? Can I just set up a recurring cron schedule for it to run every so often?
As per my further investigation, the action that is called when you click on the button "Check for missing cache entires" is "wpv_maps_check_missing_cache".
You can find reference related to action within the following file where you can see the CRON related information as well.
=> plugins\toolset-maps\includes\toolset-maps-views.class.php
Lets say when you click on the button "Check for missing cache entires" and there were 500 missing address found then it will process the 50 and for remaining it will start the CRON that will run every hour and process another 50 records.