Working with the Zendesk <> PagerDuty integration -- Custom Trigger for automated public reply?

Hi! We've recently set up the integration between Zendesk & PagerDuty. We have a set of conditions such that if a particular custom form is used to create a Zendesk ticket with a particular priority level selected, PagerDuty gets pinged. This way, our on-call engineer can be notified during off-hours when there are no Support Agents available to triage and escalate. 

I'm wondering if it's possible to create a trigger that will send an automated response back to the customer once the on-call engineer has updated the PagerDuty status to “acknowledged”? Essentially, we want the customer to at least get an email that says something like “An engineer has received your request and is currently investigating it” without the engineer logging into Zendesk or communicating directly with the customer.  I don't want to send this message in the initial automated response that gets sent as a result of the ticket coming in because I want it to actually be true. So it really needs to be based on an action in PagerDuty from the on-call engineer.  Is this possible? Has anyone done something similar?