A number of members were absent
The number of elderly is rising

WW, this example I think, sums up the argument quite effectively. It appears to me, that the article ahead of, 'number of' is important to the determination of the plurality of the verb.

Thus,
'THE number of', is used with a singular verb and,
'A number of', is used with a plural verb.

Using the example above, if the article is THE, then the noun, NUMBER determines the verb. 'The number of', is a singular collective noun. Whereas, if the article is A, then the noun MEMBERS, will qualify the verb.

To my mind, therefore, the 'of members' part of the sentence cannot be left to be understood, since, it is an important determinant of the state of the verb.