All the best to you too, Casi?me either pops up in that context, yes. Ellipsis is the culprit:
A: It doesn't work for me.
B: (It doesn't work for) me, either. / Me, either.
A: I don't like it.
B: (As for) me, (I don't like it) either.
A: I haven't seen the film.
B: (As for) me, (I haven't seen the film) either.
The question is, however, is shortened me, either considered standard usage in those contexts? (Google doesn't help us on that one, riverkid.)
What would help us in this case, Casi? There is a great deal of ellipsis in speech and it's completely unremarkable. How many times must it be said; the rules of Standard English do not describe the rules for speech.
You've shown us with your analysis above just how completely natural 'me either' is.
On a related topic, would you say both Neither do I (post #4) and Either do I work as responses for "I don't like it"? Why or why not? If yes, is Either do I considered standard usage?
Please note that, dihen asked, "Should I say...?", not What do people say? Dihen is aware that there's a variation out there - hence the question.
Did I suggest that 'either do I' is an idiomatic response? When ESLs ask such a question, they must be given an adequate reponse to let them know what to expect in all language situations.
Once again,, what grammatical reasons are there that would exclude 'me either'?
All the best.