There is not a set time. It's how much they research, I believe.

How much they research has an effect on how quickly they can master other skills such as building or healing?

No, every skill increases based on a set number of successes.

Note that some skills increase faster than others because of the time taken to achieve a success; Farmers have to walk to the food hut between successes. Builders have to carry building material. Healers have to wait for someone to get sick, once they've learned all they can learn from the plants. Researchers have it easy, only having to walk between the research hut and the table.

You can find out a lot about villager skill development in this answer in our Support FAQ.