This is a good guess, and I think it's noteworthy that this happens even if the variable appears to be being set before use Module:

$ perl -I. -wMstrict -le '$Module::configvar=1;
    use Module; Module::menu();'
in Module: false
in menu(): true
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Because use gets run in an implicit BEGIN block, so the code in Module.pm will always be executed before the code that sets $Module::configvar=1;. One solution is to say BEGIN { $Module::configvar=1; } before use Module;.