either/neither when alone are always singular. So I'd go for "does" typically. But it may not be straightforward in all cases though.
You do your homework
You does your homework
First one is right, so does it make using "do" here in the sentence right. If it was "either of you", would u still have used "does"? That would sound totally wrong though.
Moreover,
As a subject, “either” is singular. it’s the opposite of “both,” and refers to one at a time: “Either ketchup or mustard is good on a hot dog.” But if “either” is modifying a subject in an “either . . . or” phrase, then the number of the verb is determined by the number of the second noun: “Either the puppy or the twins seem to need my attention every other minute.”
Dont you think "us" is the subject here and not "either"?
I would go for "DO"