Cunicular simply means “rabbit-like”. I recently came across this very rare word in an science-fictional work:
If it was hard being a small boy in a time of rapid change, it was a doubly hard burden to be a meter-tall rabbit cursed with human sentience and cunicular instincts.
Singularity Sky, by Charles Stross, 2003.
It would take too long to explain the background to this Carrollian image — you’ll just have to read the book. The rabbit does have a waistcoat, but no pocket watch is mentioned.
Cunicular is better known to biologists than to SF authors. It derives from Latin cuniculus, rabbit (itself taken from Green kyniklos), which is also the source of the old English name for the animal, coney or cony. The Latin word could also mean a burrow, an underground passage, or a military mine. Variations on it appear in systematic scientific names — an American owl, to take one example, is formally known as Speotyto cunicularia because it lives in burrows.
Cunicular has occasionally been used in botany and medicine for various kinds of tubular formation. Apart from that, sightings are extremely rare. This is one of the few, from a description of an old Spanish method of hunting hawks by imitating the distress call of a rabbit:
A crab's claw, or the green bark of a two-inch twig slipped off its stalk, will, in the lips of an adept, produce just such a cry of cunicular distress.
Unexplored Spain, by Abel Chapman and Walter J Buck, 1910.