I topped my papaya and covered the top with plastic. Multiple shoots growing on the trunk which I will trim to just a few of the strongest. How long should I leave the top covered with the plastic?

You should remove it right away. The plastic could cause the trunk to rot. You want it to dry out and callus over.

I live in a tropical zone and have never heard of topping papaya trees, much less, this method of placing plastic to cover papaya trees. This is definitely something new to me! : Please enlighten us by providing your zone/area, and where your information of caring for papayas came from.