The correct option is A seems
It is to be kept in mind that Either, Neither, Each, Everyone, Many a, must be followed by a singular verb.
'Neither person' means none of the persons. So, we have to consider both of the persons individually. By the general convention, a singular noun takes a singular verb. Thus, Option A 'seems' is correct and Option B 'seem' is incorrect.
Options C and D are incorrect as both 'were' and 'have' are plural verbs.