If $new_mail needs to be shared between two object methods, it makes sense to me to make $new_mail an attribute of the class you're in. (It's irrelevant if it's class data or instance data.)

Now, the question probably becomes "How do I make class data"? The best answer to that that I've found is to simply make a file-scoped lexical. You do have inheritance questions if you want children access to class data of their parents, but that's an implementation question. :-)

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We are the carpenters and bricklayers of the Information Age.

Don't go borrowing trouble. For programmers, this means Worry only about what you need to implement.