You already backed up STDOUT in $stdout. So all you need to do to print to STDOUT only is:

open(  $stdout , ">&STDOUT" );
open(  $stderr , ">&STDERR" );
open( STDOUT , "| perl tee.pl -a $fErrorLogFile" );
select STDOUT; $| = 1;

print "Some text....\n";
..
..
code
..
..

select $stdout;
print "Some other text....\n";
[download]

Note that you might have some buffering problems here.

--
Leviathan