The problem came in when I tried to do the same with STDERR. In this case all the output from STDERR disappeared. If I swapped the STDERR and STDOUT ties done in this manner, I would then get STDERR output and not STDOUT.

That's because you are essentially doing:

perl -we'open FOO, "> baz"; open BAR, "> baz"; print FOO "one\n"; prin
+t BAR "one\n";'
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where FOO and BAR have independent file pointers into the same file. If you want to share a logfile between two handles, use >> to force all writes to append at the end, or open the file outside the tie handler and pass its glob to your logger.

This works for me:

use InstallerHandleTie;

my $gfh = *STDOUT;
my $geh = *STDERR;

foreach my $outfile (qw/log1 log2/) {
        open my $outfh, ">", $outfile or die "nope: $!";

   local *STDOUT;
   local *STDERR;

      tie *STDOUT, 'InstallerHandleTie', $outfh, $gfh;
      tie *STDERR, 'InstallerHandleTie', $outfh, $geh;
      print "Writing to $outfile\n";
      warn "Writing warning to $outfile\n";
      untie *STDOUT;
      untie *STDERR;
}
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