my (@array, $keep);
while (<$handle>) {
    if (!@array) {$keep = /FIRST_PATTERN/;}
    next unless $keep; # Next if we haven't seen the first pattern.
    push @array, $_;
    next unless $keep = !/SECOND_PATTERN/;
                       # Next unless the second pattern is seen.
    process_array \@array; # Process and print
    print @array;
    @array = ();
}