I would pick one person at random and ask him to identify each of the 10 people. If he was the liar, he would tell me that 8 of the people were village members, that he was the truth teller, and that the truth teller was the liar.
If he was the truth teller, he would tell me that 8 of the people were outcasts, and that he was the truth teller, and that the liar was the liar.
If I picked one of the outcasts, and they were lying, he would tell me that he was a village member, point out 7 other village members, and then identify the truth teller as a liar, and the liar as the truth teller.
If I picked one of the outcasts, and they were telling the truth, he would identify himself as an outcast, point out the other 7 outcasts, and identify the truth teller and the liar as their respective selves.
Any way I know exactly who the truth teller is, and would ask him or her for directions.
Unless, of course, you could each act of 'identifying' as alternating between lying and being honest. But as long as they do it in once sentence, I say it's all one event. I'd just ask him to talk in a single sentence.