"a majority of" vs "a percentage of"

English as a Second Language English Vocabulary, Grammar and Idioms
1

Is there any general rule of thumb regarding the verb form when “a majority of/ a percentage of” is used in a sentence:

Is it correct to say: A majority of railway commuters reads or listens to music while traveling?

2

.
Majority and percentage are both singular nouns grammatically, but in language use, the following noun often determines the number of the verb, through the processes of proximal and notional agreement:

A percentage of the wine was tainted.
A majority of the vintners were arrested.
.

3

since in the above sentence commuters is plural the verb should take plural form:

is the corrected sentence be:

A majority of railway commuters read or listen to music while traveling?

4

.

.