Non Perl answer:

Use SSI if it is enabled on your web host. and included the follwing in your html.

  <!--#echo var="LAST_MODIFIED"-->.
[download]

or

  <!--#flastmod file="mypagename.shtml" -->
[download]

From Apache.org and Microsoft

To do this in perl on static pages you would need ssi enabled and ssi has built in functions to do it so the script would not be needed.

Update: For clarity the last paragraph should probably best read.
To do this in perl on static pages you would need ssi enabled. Because ssi has built in functions to do it, you would not need a perl script to create this.