OK, so if do you want to have the report results dynamically filter as you type, rather than use a search widget on the dashboard, I suggest you simply put a button there which will run a "list all" customer report, And as these executives start to type the list will get shorter.
The Browse choices pop up window comes up if you force what is called the record picker or if you have more than 1,000 record to chose from. You are correct, that does not dynamically filter. I agree that would be a nice feature, so User Voice is an option to request that enhancements and then try to get Forum users to vote for it.
