Finding file in parent folder of an AppleScript
Here is an answer to get right the pathname of .. from AppleScript:

Get Current Path to Script within AppleScript and Append Subdirectory

Anyway, the actual construct you got: /path/to/folder//myscript.pl
is a correct pathname to your Perl script. The 1st / is coming from the terminal one coming from container: /path/to/folder/.

Hence your built find command is very similar to this one you might try
to experiment:

find ~/ -name "Documents" -print


Hint: work directly in Perl, it is many times more efficient than any AppleScript.