Post is correct. It is a specific job. Occupation is more general.

I think I disagree with Cyris' answer. I would say that "post" refers to a specific employment position that requires one person's labor. For example, let's look at this sentence: There are five teaching posts at the school. This means that there are five employment positions at this school that require a teacher who can do the work. Once they've hired five people, all the posts are filled. They don't need to hire anyone else. If they only have four teachers, there's an available post at the school. "Occupation" is a general term referring to the type of job one does. Example: A: What's your occupation? B: I'm a teacher. You could also say "I'm a doctor," "I'm a lawyer," "I'm a baseball player," "I'm a painter," etc. Those are all different occupations. Does that make more sense?

Start thinking a bit! A post is something that stands in the ground, and is vertical. This image is enough to convey the difference between "post" and "occupation". A "post" is a position, where soldiers stand guard. A little bit of imagination, thinking a bit, and you can't confuse these two words. Clearly, you occupy a post, just like you occupy any space or position.

Thanks Trillian, I think I have heard "teaching posts" used to mean college tenure positions. Do you think we also use this phrase to refer to any other kind of teaching jobs?

There is nothing wrong with the question. It is not a tricky question at all. The term "teaching post" is commonly used.