Hey Robert,
Well the direct call rule itself could fire an Analytics beacon in addition to deploying the pop up. To do that, you'd just need to use the Adobe Analytics section of the direct call rule. This would allow you to send a beacon every time the pop up was triggered. If you wanted to track engagement within the pop up window itself, that might be a bit more tricky. Is the pop up loading some sort of iframe or what content is being displayed in the pop up?
Thanks,
Jantzen