Yes, that does make more sense. Just one word of caution though... Instead of this:

    # Interval to change at if we want $mode = "running"
    my $interval = $ARGV[0];

    # Change the mode if we have been passed an interval
    $mode = "running" if ($interval);
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something like this would be more prudent:

my $interval = 0;
if ( @ARGV ) {
    ( $interval ) = ( $ARGV[0] =~ /(\d+)/ )
        or die "Usage: $0 [m]\n m: number of minutes between color cha
+nges\n";
}
$mode = "running" if ( $interval );
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That makes sure that you don't try to do arithmetic on a non-numeric string, or sleep for a negative number of seconds.

(update -- minor nit-pick -- since you now have an "interval" variable that is either true or false, you don't really need a "mode" variable, do you?)