brain / brains

[Tedwonny]

I came across this sentence:

He's a big strapping guy but short on brains.

I look the word 'brains' up in Cambridge dictionaries online:

[C] used to refer to intelligenceMarie has an amazing brain (= is very intelligent).
That can't possibly be the right way to do it - use your brain!
The poor child inherited his mother's brains and his father's looks.
He's got brains but he's too lazy to use them (= He is clever but lazy).

and I still don't quite understand why 's' is needed after brain.
If I use the singular form - short on brain - would that be okay?

How do native speakers judge when to use the plural/singular form? Thanks

[Tdol]

If I use the singular form - short on brain - would that be okay?

No, it wouldn't. It's a tricky question, but it's largely down to collocation. If you're thinking about intelligence in general, the plural is more likely. If you're thinking about the person's whole mental capacity as a singular entity or their focus on a singular issue, then the singular is more likely. Other people may see things differently.