grammatical number - Is 'rest' singular or plural?

When 'rest' means what is left after everything or everyone has gone, been used, dealt with, or mentioned, is it singular or plural?

My guess is, this depends. When 'rest' refers to countable things and the number is more than one, it is plural; otherwise it is singular.

For example,
suppose there are five boxes. You carry two; then there are three left. We can say 'the rest ARE three.'
suppose there is one bottle of salt. You sprinkle some; then there is less salt. We can say 'the rest IS less than one bottle.'
Is my description correct?