position/s

Pronoun and verb = two things = plural

Therefore positions with an 's'.

To clarify...

The pronoun has (sing.) changed its (sing.) position (sing.) to that (sing.) previously occupied by the verb, which has (sing.) moved to that (sing.) held by the pronoun. They (pl.) have (pl.) exchanged positions. (pl.)

N.B. In my eyes, "switched" with this meaning is slangy AmE for "exchanged".

Many thanks to your reply with the illustration. It makes it easier to understand.

Best wishes