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I setup my "background.pl" script in the scheduler to run every 5 minutes (or something like that). It looks in a predefined folder for files to act on. For example, let's say these files (named with the date/time) exist in the folder:
If "background.pl" doesn't find any files, fine, it just exits.
Once that's working, then you just need to write your Perl CGI script so that its only job is to create these files in the specified folder. Therefore, it doesn't actually have to kick off the background process itself. It just creates the files, maybe based on form input, and provides its response to the user. And you will know that this submission will be handled within 5 minutes.
Naming the files with date and time helps to insure unique file names, though it won't work well if two submissions happen at the same time. Even better would be to use a counter. Or, Apache has an environment variable named UNIQUE_ID which is ideal for this; maybe IIS has something similar.