I'm testing.... No problem so far (but I replaced the "remote script" by the simple straight commmand : tar czf  /tmp/toto.tgz /mnt/Musique/AlJarreau/Jarreau/
May be the remote script is hosed... Why use "print STDERR"? You have "warn" for that, use it.
BTW you didn't follow the Very Holy Golden Law : Always Use strict.
Better change the code this way :

#!/usr/bin/perl -w
use strict;
use diagnostics;
#use strict;
use Net::SSH::Perl;
use IO::Handle;

open(FOUT, ">/tmp/test.out");
open(FERR, ">/tmp/test1.err");

##########################

my ($sshconn, $ssherr, $sshexit);

my %params = (    protocol => 2,
                port => 22,
                debug => 'true',
                interactive => 'false',
                compression => 'false',
                identity_files => [$ENV{HOME}."/.ssh/id_rsa"],
                options => [    "RSAAuthentication yes", 
                                "PasswordAuthentication yes", 
                                "ConnectTimeout 10",
                                "BatchMode yes",
                                "FallBackToRsh no",
                                "RhostsAuthentication no",
                                "RhostsRSAAuthentication no",
                                "KeepAlive yes"]
            );

eval
{
    if ( $sshconn = Net::SSH::Perl->new("localhost", %params))
    {    

        $sshconn->login('op');
    
        $sshconn->register_handler("stdout", sub {
                my($outchannel, $outbuffer) = @_;
                print(FOUT $sshconn->type);
            });

        $sshconn->register_handler("stderr", sub {
                my($errchannel, $errbuffer) = @_;
                print(FERR $errbuffer->bytes);
            });

        ($ssherr, $ssherr, $sshexit) = $sshconn->cmd("/tmp/bufile.pl")
+;                
    
        $sshconn->cmd("exit"); 
    }
};

if ( $@ )
{ 
    warn $@;
}


close(FOUT);
close(FERR);
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