Answer
Set it up on the Customer record: under the Customer's Address tab, go to General Address Info and add an email-type Comm(unication) Method, then go to the Address tab's Order Address Info and set that email Comm Method as the Customer Contact. That flows through to the Reference and Reference Name fields on Customer Order, and from there to the Cust Reference field on Customer Invoice — which is what PDF_PARAMETER1 for the invoice report actually reads its email address from. Without that Comm Method set up as the Customer Contact on the Order Address, PDF_PARAMETER1 has nothing to populate from and comes through null.