What you're doing seems very odd. Perhaps you should have a slightly more complex data structure to associate those magic numbers with the variables they correspond with.

One major thing you're doing wrong is using numeric comparisons (!=) when you should be doing string comparisons (ne). You are also overwriting $tkt_data instead of appending to it.

This is untested, but might do what you want. Season to taste.

my @ar = (
  ['2',         $p_suby],
  ['7',         $p_stat],
  ['8',         $p_desc],
  ['536870915', $p_catg],
  ['536870922', $p_agrp],
  ['536870926', $p_lnam]
);
my $tkt_data = '';
for (@ar) {
  if ($_->[1] ne '') {
    $tkt_data .= ',' if $tkt_data ne '';
    $tkt_data .= sprintf('"%s%", "%s"', @$_);
  }
}
[download]

Alternatively,

my $tkt_data = join ',' =>
    map(sprintf('"%s%", "%s"', @$_) =>
        grep($_->[1] ne '', @ar));
[download]