We explain to our Spanish speaking English students that if you want to say ‘yo tampoco!’ by itself we use the expression ‘me neither!’ Followed by an affirmation such as ‘yo tampoco quiero ir’ or ‘nosotros tampoco comemos gluten’, we cannot use ‘neither’. We have to introduce the positive form ‘either’. So for the aforementioned examples we’d say: ‘I don’t want to go either’ and ‘we don’t eat gluten either’. We cannot use ‘neither’ when there is already a negation (not) in the sentence since ‘neither’ is a negation and we must not employ a double negative in a sentence in English. Hope this helps. Let me know if you have any doubts!