Answer:
This sentence has a mixed compound subject connected by nor, so the verb agrees with the singular subject that is closer.
Step-by-step explanation:
In the given sentence,
"Neither the council members nor the mayor supports the new parking restrictions."
the sentence uses the comparative "neither......nor" form where the sentence is more of the negative sense.
With this use of comparative form, the use of the word "nor' in the sentence as a connection makes the use of the verb in the sentence right. With the connecting word "nor", the verb used will agree with the subject that is closer to it, i.e, "the mayor" which is singular. Verbs in this type of comparative forms will take the side of the subject nearest to it.
Thus, the correct answer is the first option.