Ok, to call a rule you need an action, think if this (rule) then that (action).
For your example you want to have an action to print a document.
Find your print action and right click clone it, in the settings menu change the printer job to the copy of the configuration you made, you will need to create a new printer job for this. Make sure you set it to a name you remember
Now goto rules and create a new rule, In the rule type choose Automation Command Executed Event, in the settings choose “Command Name” = "Whatever the custom buutton on nav screen is"
And finally choose the action youve just made, if you need to see a scrreenshot tutorial I can make one up.