Mike - I have experience with this a couple ways...
I organized our food truck event at Davis Camp in 2016 and 2017, attached our application for your reference. We required a permit and small fee for the event, in addition to the Health Department's permit and a COI for liability. Everything was first-come; first served on the vendor's side. In the event of multiple vendors serving the same type of food- I didn't exclude any vendors in the selection process, but I did make subsequent vendors aware that there would be competition so they could determine whether or not they wanted to attend.
For a more permanent vendor solution, the County offers an annual vendor pass, for $500 annually a vendor can come into our regional parks and serve the public (in addition to health permits, and COI). The fees are small relative to other areas of the state, as we found this to be what the market will support. We also see this as a value adding service to our visitors, which increases revenue at the gate.
With regard to Health Department, the County has two avenue for permitting the food vendors: mobile vending license/permit; or event-based vending permit.
If you have any other questions, I am happy to help.
Jeremy