Compare 2a to 2b. The subject of the infinitive verb go in these need only be expressed in the surface structure if that subject is different from the previous antecedent subject of the complement verb want or the nearest antecedent will be the subject of any verb unless there is specific information to the contrary, say due to ideosyncratic features of the verb.
So it is possible for an implicit unstated subject to be the subject of go in 2a and needs to be an explicit subject in 2b.