my $file = shift @ARGV;

if (open my $FH , $file) {
    my $start_pattern_found = 0;
    while (my $line = <$FH>) {
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It's a side note, but I can't understand why you do this. You just want to show the use of a flag, which is a good point. Since the example may very well stay minimal, why not using good old <> instead?

In any case, using the range operator in scalar context may be much easier than maintaining a flag yourself:

while (<>) {
    chomp;
    next if 1 .. /^internal name/;
    print "Found pattern at line $.\n" if /^need this/;
}
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