Your code seems to work for me, but I am on Perl v5.12.2. Your version is very old. I recommend updating your Perl version to eliminate this as a variable. Here is what I get:
perldoc -t test.pl
NAME
SYNOPSIS
This is a normal paragraph of text. A second line to test if the
paragraph wraps with the previous one.
/tmp/Rr4_NPU0ZN (END)
I think you can get rid of the =pod . See also: ENVIRONMENT. What about perldoc -T ?
UPDATE: As it happens, I also have v5.8.8 installed, and I get the same results as I do with 5.12. It works for me with both versions of Perl.