When I run your code:

use Getopt::Long;

my ( $timeout, $show_help ) = 30;
unless ( GetOptions("timeout|t=i" => \$timeout, "help|h|?" => \$show_h
+elp) && $show_help ) {
    error_info();
}
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I get the following output:

Undefined subroutine &main::error_info called at tmp.pl line 5. </c>

This is what I expect. If I call your script with --help like this:

perl -w tmp.pl --help
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I get no output. This is also what I expect, because your && expression is not true ($show_help and GetOptions will be true, which never satisfies an unless statement).

Maybe you want to use less clever code like the approach outlined in the documentation of Getopt::Long?

use Getopt::Long;

GetOptions(
    "timeout|t=i" => \my $timeout,
    "help|h|?" => \my $show_help
) or die "bad options.";

$timeout ||= 30;

if ( $show_help ) {
    print "Showing help\n";
    error_info();
}
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