You have had solid answers to your question. Let me take a slightly different tack.
First, the word presence here has a special sense,
Also ‘a’ is also being used in a special way. It is not like ‘a pear’ or ‘a sports car’. it is in a deeper way ‘indefinite’. It has the sense of ‘some undefined’ or ‘some unstated’... Ancient Greek and Latin had words that did this job. In Greek the word was ‘τις’ (tis). In Latin it was ‘quidam’. Both were enclytic (followed the noun they qualified.).
Praesentia quaedam or παρουσία / επιφάνεια τις
School kids of my generation were taught to translate these as ‘a certain, conveying something undefined or (literally)* indefinite*.
So because the presence is undefined, it cannot be counted. Perhaps the presence of one or of several *whatever-it-ises *. All the character is aware of is a presence.