Make a text constant with the name of the "button". Add a new field to the Request Page. SourceExpression is this text constant. Name and Caption empty, as in '', empty string, two apostrophes. Write your code into the OnDrillDown trigger. It will make the SourceExpression appear much like a hyperlink, the user clicks it, the code is ran.
Confirmed in NAV2016. Not sure about Business Central / AL.
Example use case: autofilling some fields/filters.