First I don't know how many lightning strikes you get in your area but I would not bother. A couple of really long bolts into the concrete and I'd be happy.
If lightning is a real probability. IE there are regular strikes near or on your property then a rod closer than 4' is OK but to do it right I think you need 2 down conductors and that might require 2 rods. The lightning down wires should be as free from bends as possible and the rods should be located very close to the building. Lightning does not tend to turn corners and will just as likely follow the skin of the building. You also need to bond the lightning ground rods to the main electrical electrodes. I might be inclined to install a tvss at the circuits entry to the house or on the service.
Is your house lightning protected? is a tvss installed in your service panel?
I doubt the gazebo is any more likely to be struck than your house or the hydro poles or any trees in the area.
My advice is tempered by the fact that lightning is rare where i live but even in Alberta Where we got lots of lightning I would not have bothered. All of this is subject to the highest point disclaimer. If the gazebo is built at the top of a hill all bets are off.
