It appears the OED proposes two areas of meaning:
- Senses relating to spittle or mucus
- Senses referring to the slavering utterance, etc. of infants, and weak-minded persons - a transferred sense. [OED] (Subscription required)
The OED cites Langland’s Piers Plowman (1362 - OED’s date) as the earliest source for either sense in Middle English. The OED also cites a recorded usage in Old English for the first sense, at around 1000 C.E., though this might not necessarily mean that the second sense would not have been in use simultaneously.
The first sense (Senses relating to spittle or mucus), according to the OED, includes the obsolete and transferred, for instance related to water, meanings of ‘to let flow out of a crack’ (1707 J. Stevens tr. F. de Quevedo Comical Wks. 481 This crack'd Pot..drivels out the Water.), transitive, and of ‘to flow ineptly’ (a1774 O. Goldsmith Surv. Exper. Philos. (1776) I. 404 The water..will not spout at all, but drivel down the side of the vessel.), intransitive.
The OED also advises that the second area of meaning is somewhat broader: it is not only ‘to talk in a childish, or idiotic way’, but also ‘to waste or fritter away in a childish or idiotic manner”, transitive, and ‘to go on in a feeble or idiotic manner’, intransitive. 1878 R. W. Emerson Fort. Repub. in Wks. (1906) III. 391 Drivelling and huckstering away..every principle of humanity. 1885 Law Times 23 May 68/2 He drivels on from year to year, his fine abilities rusting from disuse.
In your example “'The waves hardly made any noise as they struck the cliff, and they drivelled backwards slowly'.”, ‘drivelled’ is intransitive. Though the author does not use ‘drivel on’ but ‘drivel backwards’, perhaps the sense ‘to go on in a feeble manner’ might still speak to the author's intended meaning. At the same time, ‘to flow ineptly’ - the obsolete, according to the OED, transferred usage in the first area of senses - also conveys a closely related idea.
Some other interesting examples of usage:
Byron, Don Juan:
We learn from Horace, 'Homer sometimes sleeps;'
We feel without him, Wordsworth sometimes wakes,--
To show with what complacency he creeps,
With his dear 'Waggoners,' around his lakes.
He wishes for 'a boat' to sail the deeps--
Of ocean?--No, of air; and then he makes
Another outcry for 'a little boat,'
And drivels seas to set it well afloat.
Emerson, The Conduct of Life:
The devotion to these vines and
trees he finds poisonous. Long free walks, a circuit of miles, free his
brain, and serve his body. Long marches are no hardship to him. He
believes he composes easily on the hills. But this pottering in a few
square yards of garden is dispiriting and drivelling. The smell of the
plants has drugged him, and robbed him of energy. He finds a catalepsy
in his bones. He grows peevish and poor-spirited.
Shakespeare, Romeo and Juliet:
Why, is not this better now than groaning for love? Now art thou
sociable, now art thou Romeo; not art thou what thou art, by art as
well as by nature. For this drivelling love is like a great natural,
that runs lolling up and down to hide his bauble in a hole.
There are many other examples. I was able to locate these though https://quotations.ch
This is something I have designed recently with a great deal of help from a friend. Not all authors are in the unrestricted access area, though many are, but if you would like me to look anything up, you are welcome to let know.