Regardless of official versions from Taylor's site (boiled linseed oil, and do be careful on light-colored wood inlays, as they aren't sealed or protected, can and will get a lot darker.,) here's my take on it, based on simple science rather than propaganda:
Wood has natural oils in varying degrees. Some woods are so oily that it's difficult to even get the glue to hold them in place. Your ebony fretboard on a Taylor guitar doesn't actually need any more oil. Why not? 1) Oil does not evaporate. Water/moisture does. Quite the contrary, the oil on our fingers adds to what's already there. So if your wood looks dry or is shrinking, that's either a humidity issue or oxygen/aging. In either case, a bit of light rubbing with 0000 steel wool will tend to that problem. (Be sure to take some blue painter's tape and put it over the soundhole and any other areas that might get tiny pieces of steel in them.)
Shrinkage is a real thing. I can recall one winter with an unbound fretboard and sliding my hand up the neck and slicing my finger open on a fret that was protruding because the neck had shrunk from being too dry. But oiling the fretboard isn't the solution. Correcting your humidity is. 45-55% is what Taylor recommends. Anything under 40 for an extended period of time is pushing your luck, and not just on the fretboard, but also on your bracing, and other unsealed structures.
This is my first post here on such a subject. Feel free to ask or discuss politely.