The Inactivity Timeout is a fixed value, and you can't easily reset it for different times of the day. You can, however, fairly easily control which times of the day alerts are actually sent, based on a variety of criteria:
The TimeIsBetween() and DayIsAWeekDay() functions in the screenshot above are relatively simple custom methods in a class that extends Ens.Rule.FunctionSet, which makes them selectable in the rule editor's function editor dropdown. I wrote them simply for the improved readability they provide for the routing rule.
In the rule above, alerts for the HIE_ADT_out interface are sent only between 7am and 7pm to the Integration team; on weekdays only the help desk is included. Any that fall outside of that timeframe are discarded.