Does calling it vars.conf and not putting a perl interpreter call into it, make a difference? (In other words would it work better if I made it vars.cgi and put the #! shebang line in it?)

No no, you definitely want to require it. As a require'd file, the shebang line and filename "extension" are not special.

As for what's really going wrong, it's hard to say without seeing more of your code.