I like an interesting spin on a 'traditional' god of knowledge ..
The concept behind it is .. gaining knowledge can be done two ways, firstly by paying the 'iron price' and learning through observation, action and experimentation (experience). The second is by transferring knowledge from a higher power (or perhaps imprinted on tomes/objects/special places/rituals). The problem is.. that when you 'transfer' power you are getting someone elses experience .. and a bit of them comes with the knowledge .. a bit of their emotions, a bit of their essence is tied into that learning .. often this causes a sense that you are not alone, that you have been violated .. and in the worst cases madness/split personalities, etc.
The core personality of such a god is someone who is a collector of knowledge .. perhaps they view it as their duty .. perhaps it is simply an obsession. A 'sage' stereotype but with deeper layers of confusion, insanity, unpredictability. Asking questions about common knowlege is likely to be fine, but knowledge known to few is more likely to draw out those deeper personalities.
Regarding travelling or wilderness god's ..
I also like animal aspects to gods with a link to humanity. The idea of a wild bear coming across a child who has strayed into the deep forest. Exhausted the child can only cry as the bear closes. The bear senses the sorrow and pain in the child and goes against it's nature and protects the child, diging into the frozen earth (bloodying it's paws) and laying partly over the child to keep them warm. Hunters come seeking the missing child and finding the bear and thinking the bear has killed the child disable the bear with mortal wounds while the bear stands over the unconsious child defending it. The child is found beneath the bear to be alive, and one of the hunters (mother to the child), moves close to the injured bear (placing themselves in danger) to end the bears life peacefully. As the bear spirit rises the mother gives thanks to the bear and gives he heart to it, her strong emotions allow the bear spirit to linger .. over the coming years, the village offering prayers to the bear as thanks and out of respect to it saving the child and it becomes empowered. It is a wild god, that stalks the wilderness .. but it now it watches over lone travellers and small parties .. also polar bears rock!