When two (or more) people take a short vacation soley for the purpose of getting away from their children, friends, or relatives in order to have private time for sex.
Shawn's parents are on a sexcursion, we should have a party!
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When two (or more) people take time out of their day to fuck in a public place. Or when said people ignore commitments in order to get some action.
Hunter and Gabby had a sexcursion at the local Barnes and Noble; It got very spicy, much like the food you would find in Honduras.