Merriam-Webster Learner's Dictionary gives the two examples for livestock:
However, it does not assign countness / non-countness here in accordance with how CGEL regards it. Since neither sentence accepts a numeral or equivalent
*a market where three livestock/s are bought and sold
*a market where a dozen livestock/s is bought and sold
the usages must both be deemed non-count.
The correct way to describe these usages is 'used with either a singular or a plural verb-form'.
Also, comparing with the unacceptable notional plural form 'livestocks', 'livestock' is of singular form (no -s).
Note also that 'livestock' refers to an etically countable referent, perhaps 20 cows and 50 sheep.
Various dictionaries wrongly or unclearly address these issues.
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CED merely labels stock in the cattle etc sense 'plural'; as the plural form 'stocks' is available with other senses of the word, CED obviously means 'treated as plural' or better 'taking a plural verb-form'.