I am trying to put an option into my perlscripts which allows for a debugging switch which, when submitted to the script, prints out debugging messages.

It seems like you don't want a constants, because constants tend to never change. Constants should also not be influenced by external circumstances. Try using a variable instead, like $DEBUG.

And "constant debugging" sounds like a 24/7 job :)

If you decide to use a constant after all (bad idea, imho), you could delay definition until @ARGV is fully parsed, and then use use constant DEBUGGING => $minus_d_found;

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