Why would the parking and dash lights come on when '97 Aerostar is turned off and key is removed?

In my experiences with Aerostars, your "problem" is actually a feature. It is a safety measure to ensure that you can see to your destination without tripping on things if they shut off after let's say 3-5 minutes it is just a feature to ensure your safety. Reading the owner's manual or investing in a Haynes Repair Manual will further investigate this "problem" and give you a solution.