There's no built-in feature in Kayako that allows you to set a countdown timer for the desired time to be spent on each conversation. But, you can set up an SLA which gives you the option to set the first reply time, next reply time, and resolution time of a conversation.
SLA establishes and monitors target times for when your team should be responding to and resolving their conversations. For any conversation that is subject to an SLA, you'll see a countdown timer that shows where a conversation is at its targets in the top toolbar.
For more information about this, please visit the Establishing SLAs article.