Which Event Type should be used for when a case is updated by E-mail

Hello,

I'm somewhat new to SuiteScript but I'm pretty familiar with coding.  I don't believe I have any scripting errors here, but I can't figure out which "Event Type" to use in my script deployment to get it to run when a case is updated via client e-mail.  My code is below:

function onCaseUpdate()
{
var record = nlapiGetNewRecord();
  
var status = record.getFieldValue('status');
if((status == "7") || (status == "6")){
  record.setFieldValue('status', 4);
}

return;
}

Currently I have this deployed as:

Applies To: Case
Deployed: Yes
Status: Released
Event Type: Email

This deployment does absolutely nothing.  If I set the Event Type to "Edit" then the script runs when editing/saving a case; however, none of the Event Types I've tried cause the script to execute when a client updates the case via e-mail (ie. replies to an e-mail that was generated by the case).