You could only build it on a village claim and it would provide a tiny buff while on that vclaim. Originally I thought the buff should be learning ability, but I don't want it to be vital for powergaming, so perhaps instead the buff should be random, rolled at a set period of time and perhaps consistent across all Wicker Men globally. Slightly increased walk speed, +1 to +5 on a random stat, animals eat slightly less, etc.
You could lift and drop whole logs into it. Additional fuel would cause it to burn for longer. I'd like it to burn for at least an entire week with full fuel, and be able to take a significant number of logs. This makes it more of an interesting afterthought. Fuel quality and quantity do not effect burn time or buffs in any way, shape, or form. The Wicker Man could give off a significant light, illuminating a good portion of a village for the larpers out there.
In an ode to the Wicker Man's original purpose (human sacrifice), you could throw skeletons into it. This should provided a miniscule boost to the buff. This boost should be so small that you seriously consider burying the body for the experience hit. This prevents abusing wilderness beacons and the formation of death cults. Honestly not a big fan of this but adding this paragraph might stifle the few neopagans crying mUh ReAlIsM.
Multiple Wicker Men could be built. The effects would not stack so this would be purely for aesthetics or if you have a desperate need to destroy logs. Perhaps you could also build them off claim, which offer no buff but are excellent for threatening people.
or just let us stick whole logs in tar kilns ololololololo