You are nearly there with your remark about the word perl in the shebang line. If you add a comment of the form #!perl as the second line of test.pl, the -x switch will make perl act as you want. Example:

$ cat test.pl
#!/bin/sh
#!perl
print "$ENV{PWD}\n";
$ perl test.pl
test.pl: print: command not found
$ perl -x test.pl
/home/Zaxo
$
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After Compline,
Zaxo