It wasn't until I decided to blog about an extremely seiyō kabure establishment at the top of Mt. Hiei, one of Japan's leading early centers of tōyō kabure (when it was importing Buddhism from China 1200 years ago), that I discovered a more direct source for kabure. It's from kabureru 'to break out in a rash; be (noxiously) influenced by (lacquer, poison ivy, communism, Western goods/values, etc.)'. However, I suspect that kaburu 'to cover one's head' and kabureru 'to be covered (with rash)' might ultimately be related etymologically, even though one can obscure the connection by writing kabureru with an unrelated kanji combination, 気触 lit. 'feeling+touch'. Perhaps the native Japanese root kabu in both forms even relates to the now various kabu that mean 'head' (頭), 'stump, stock' (株), or 'root, turnip' (蕪).
The place that set me off on this etymological goose-chase was the Garden Museum Hiei, which I visited because I wanted a view of Lake Biwa and because I enjoy botanical gardens. It was well worth the serendipitous visit. (I attended 2nd grade at Camp Botanical Garden in Kyoto in 1956-57, the last year before the U.S. Army closed the base and the land reverted to its earlier use, at which point several missionary families ordered Calvert School materials and started up Kyoto Christian Day School, the predecessor of what is now Kyoto International School.)
The Garden's Rose Gate faces the Kyoto side of the mountain and the Eizan Ropeway station. The Provence Gate at the other end faces the Lake Biwa side and the parking lot and bus station. I entered through the rose garden, but never made it as far as the herb garden and the Provence Gate. I was especially entranced by the water lily pond with bridges and arbors designed to replicate scenes painted by Claude Monet, one of the most Japonisme-kabure of French Impressionists. It was a Japanese tribute to French Japonisme. Carefully placed throughout the garden are large replicas on easels of famous paintings by Monet and Renoir (above all), but also Manet, Cezanne, Degas, van Gogh, and other masters of Impressionism.
It was nearly noon and I was hot and hungry, so I soon repaired to the Café de Paris for a leisurely lunch, where I ordered a bowl of Renoir's favorite cold turnip (kabu!) soup, a plate of surprisingly familiar "European-style" curry rice, and a half bottle of imported chardonnay. I was the only seiyōjin 'Westerner' in the place, but perhaps not the most seiyō kabure. A nice selection of bread rolls and a spaghetti ratatouille were the only other foods on the menu.
On my way back out, I dawdled in the rose garden, where I noticed a sign for Rosa rugosa, the Japanese rose with the incongruous name hamanasu (浜茄子) lit. 'seashore eggplant'. Not only was the plant itself awfully far from the nearest seashore, but the kanji for the 'eggplant' part of its name is another case where the kanji has no relation to the native Japanese reading (nasu or nasubi), only to the Chinese (Mandarin) reading qiezi (茄子), which shows up on so many Chinese restaurant menus in 魚香茄子 yuxiang qiezi lit. 'fish-flavor eggplant', usually translated as 'garlic eggplant' (one of my regular favorites).
UPDATE: I queried Matt of No-sword about the likely etymologies of the various kabu-. He confirmed that the various nouns kabu that mean 'head; stump, stock; root, turnip' are generally thought to come from the same etymon, but that the verbs are not likely related.
Ono Susumu says that /kabureru/ is related to /kabi/ as in mould, which kind of makes sense, but I can't find anyone who backs him up. (The Nihongogendaijiten does list a couple of unreliable sources claiming it's from 蚊触, 'mosquito-touch', which is pretty amusing.) 香触 ['fragrance-touch'] is also common.
/kaburu/ is originally from /kagafuru/ -> /kaufuru/ -> /kaburu/ ... but that was Nara-Heian times, and I don't think /kabureru/ is attested pre-Edo, so I suppose there could be a connection ... although, I can't really see how 'come out in a rash' could come out of 'cover one's head'.