What’s the right inflection for the verb “deserve” in this sentence?
When you relate two or more items with "or", you use whichever form matches the item nearest the verb. If the nearest item to the verb (which is almost always the latter or last item) is singular, you use a singular verb form. This applies no matter how many items are joined.
Contrast to "and", which is always plural because the two or more items joined all act together.
Examples of "or":
Five or six feels about right to me.
Ryan or Jack has a blue one.
One o'clock, three o'clock, or five o'clock works for me.