Step 1: Read the sentence.
The sentence is 'Neither the player nor the captain ____ attending the meeting.' We must choose the right verb form.
Step 2: Spot the structure.
The sentence joins two subjects with 'neither ... nor'. There is a special rule for such sentences.
Step 3: Recall the 'neither...nor' rule.
With 'neither ... nor', the verb agrees with the subject that is nearest to it, not with both subjects together.
Step 4: Find the nearest subject.
The two subjects are 'the player' and 'the captain'. The one closer to the blank is 'captain', and 'captain' is singular.
Step 5: Match the verb to it.
Since 'captain' is singular, we need a singular verb. Among the options, 'is' is the singular form that fits 'captain ... attending'. 'Have' and 'are' are plural, and 'has' does not fit smoothly with 'attending' here.
Step 6: State the conclusion.
The correct verb is 'is'.
\[ \boxed{\text{is}} \]