The use of bullets to divide different ideas and create a list effect
The indefinite pronoun neither is always singular.
Neither is the negative counterpart of 'either' which is also singular. The basic principle of Subject-Verb Agreement says that the subject and verb must agree with each other, so you should use a singular verb because 'either' and 'neither' are considered singular; however, this principle is sometimes broken by a plural verb which can be used after 'either' and 'neither' informally.
Jesse SWIM across, Does that sound right? NO! So cancel that word out of the selection and we are left with.. Jesse SWUM across and Jesse SWAM across. I would go with SWUM, because swam sounds more like a present kind of thing, and they are talking about last summer. So He SWUM.