use strict;
use warnings;
package TeeStdErr;
use Fcntl qw(:flock);

my $log_file = "$ENV{DOCUMENT_ROOT}/state/err.log";
open (my $orig_stderr, '>&', \*STDERR);

sub TIEHANDLE { my $i; bless \$i, shift } 

sub PRINT {
        my $r = shift;

        print $orig_stderr @_; 

        if ( open my $FH, '>>', $log_file ) { 
                flock $FH, LOCK_EX;
                print $FH "" . localtime, "\t", "ErrorLog: ", @_; 
                close $FH;
        }
        else {
                warn "Open $log_file '$!'", @_; 
        }
}

package main;
        
$| = 1; 

# Tee für STDERR
tie *STDERR, "TeeStdErr";
print STDERR "print STDERR\n";
warn "warn";