Concept:
In English grammar, the word “Neither” is treated as a singular pronoun. Therefore, it requires a singular verb. Even though the phrase “of the two candidates” refers to more than one person, the subject of the sentence is still the singular pronoun Neither.
Hence, the verb must also be singular.
Step 1: Identify the subject of the sentence.
\[
\text{Neither of the two candidates}
\]
The subject here is Neither, which is singular.
Step 2: Check the verb used in the sentence.
The sentence uses:
\[
\text{have submitted}
\]
The verb have is a plural verb.
Step 3: Determine the correct verb form.
Since the subject is singular, the correct verb should be:
\[
\text{has submitted}
\]
Thus, the correct sentence would be:
\[
\text{"Neither of the two candidates has submitted their application yet."}
\]
Step 4: Identify the incorrect part.
The grammatical error occurs in the phrase:
\[
\boxed{\text{have submitted}}
\]