@Nick ******
, A re-entry permit doesn't have many requirements. You need a valid entry stamp or extension.
What you need to know, a re-entry permit wouldn't give you extra days. For example, if you enter June on Non-O, you will get the stamp until September. And once you get a re-entry permit, it will be valid until September, the same date as your current stamp. When you enter Thailand on that re-entry permit, let's say at the end of August, you will be stamped until September, the same date on your stamp from entry in June.
General information about the re-entry permit is here.