Hello RVW
Thank you for the answer. Your thought sounds someway more reasonable. But still I cannot feel confident. If "teaching English" is appositive to "a position", I think, "She found teaching English at a high school" should be idiomatic, but it is not the case. Furthermore, we cannot use along with "a position" any noun phrase other than --ing. For example, "She found a position instruction of English at a high school" sounds weird. So…
paco