Update: :-) Unfortunately, I've tried both <> and <STDIN>, and both give the same result.

Well, try this little test:

eoftest.pl:

#!/usr/bin/perl -w
use strict;

my @lines = <STDIN>;
my $line = <STDIN>;

print @lines;
print "----\n";
print $line;
[download]

Typing in the input from the terminal works great. But here's the problem:

cat file | eoftest.pl

You'll get your uninitialized value warning there. Reason? I think it has to do with the redirection (or to be more correct, piping) of STDIN when running your script. STDIN is now a pipe from "cat file" and can't have anything more read from it - causing the warning.

Update: You may want to do something like this:
open STDIN, "/dev/pts/0";
to reopen STDIN to the correct place.

His Royal Cheeziness

Aha! Light dawns. This has the ring of truth about it. I hadn't appreciated the semi-permanent nature of these pipes.
Thanks!