A tick wound its way up his jaw

tic noun 1: local and habitual spasmodic motion of particular muscles especially of the face : TWITCHING 2: a frequent usually unconscious quirk of behavior or speech "you know" is a verbal tic m-w online

tic (n.) twitching of a facial muscle, 1822, often a shortening of tic douloureux "severe facial neuralgia," literally "painful twitch" (1798), from French tic "a twitching disease of horses" (17c.), of unknown origin. Klein suggests an imitative origin; Diez compare it to Italian ticchio "whim, caprice, ridiculous habit," itself of unknown origin. etymonline.com

I believe "tick" in the sense of "tic" is the result of confusion and poor (or no) editing. So the twitching in your example is perhaps getting more pronounced or moving higher up on his face. He has become self-conscious of it and is trying to mask it or perhaps stop it by smiling. Here "wound" (rhymes with "hound" and is the past tense of to wind--rhymes with "kind") means to move in other than a straight line. We say a river winds its way through the countryside (becomes flexuous, wanders, or meanders).

Tic is "relatively" new (despite the 1611 citations) as applied to tics in humans. Both the French and Italian "tic" lack the K, of course, and I don't see any variant spellings in the OED . My Zanichelli dictionary has "ticchio" for a condition in animals/horses and labels it rare for "tic" meaning "tic nervoso" (in humans). My Devoto-Oli Italian dictionary and the OED have an onomatopoetic origin for "tic."

The abstract of this French paper has a translation in PubMed that is très shaky, but perhaps of interest:

[The concept of tic in the history of abnormal movements] Rev Neurol (Paris). 1986;142(11):803-7.

[Article in French]
G Dordain

Abstract History of abnormal movements started during the 14th century. At that time the St Vitus' Dance was described, but the nosology of dyskinesias remained confusing during the next five centuries. The concept of tic was elaborated in France during the 18th century. It remained too large a concept however. Definitive semiologies appeared at the end of the 19th century, thus allowing tics to emerge from the "chaos of choreas". The etymology of the word "tic" still remains mysterious. In 1905, Meige thought that the word tic was used for the first time by reference to horses. He referred to the tic of the bear in the horse described by Rudler and Chomel at The Société de Neurologie de Paris in 1903. Veterinarians were thus probably the first to describe the word. If so, however, the horse must leave anteriority to the goat. The word Ticq was used in 1611 as mentioned by the French dictionary Robert. The word is said to be an onomatopea and is compared to the italian word ticchio which means caprice. Another dictionary (Littré) suggest the german word "ticken", which means "to touch slightly", the galic word tacaid (sudden pain) and the german ziki (young goat), a word which could have lead to ticchio as capra, goat in italian, gave capricio.

Speaking of capriccio (double C by the way), my feeling is that "tick" for "tic" is an orthographic caprice (polite for error) and I wouldn't vote for it as a variant spelling. I'm hesitant about hunting for more examples in print apart from the one I cited in a comment above.