I believe other Disboarders have inquired about this and have received the same response, i.e. nobody knows.
Based upon my personal observation, it is first-come, first-served. I have seen folks stake the pavilion out at 7 am. On this occasion, the people took over the whole pavilion, and entertained a big party, many of whom clearly arrived via bus from the front parking lot. When they commandeered the pavilion at 7 am, they put their stuff on all the tables, and hung decorations around the whole pavilion. They also put bags of charcoal on top of all of the grills- I assume as a sign to others to back-off because they were all taken. I thought that was very inconsiderate. They hung out there all day. A lot of times, there weren't more than a couple of people actually sitting in the pavilion.
The pavilion is an amenity available to the guests of FW. I would say if you are staying at the Fort and want to use it, then by all means do so.
These comments aren't directed at you personally, sjsinnessu, but to anyone thinking of using the pavilion to the exclusion of other guests: I don't think anyone should think it's OK to take over the whole pavilion and exclude others from using it. If you have that big of a party, reserve an extra campsite and have your party there. Or go to a public park where you live.
If you want to use a couple of tables in the pavilion, and you are willing to share with others, then go right ahead, and have a great time.
TCD