On the Waite-Smith Hermit card there is a six-pointed star lighting the lantern. Richard Roberts attributed this idea to a book which Waite translated, Musæum Hermeticum (1678).
The Hermit, too, is a transformation of the Magician/Alchemist of Key 1. Waite translated a number of books on alchemy, one of which is The Hermetic Museum (1892), the original of which was published in Frankfurt in 1678. Waite used one of the pictures from this text as a model for his hermit, without revealing it in his explanations of the Major Arcana.
As to the star in The Hermit's lantern, it is composed of two interpenetrating triangles, which have a specific alchemical meaning that we shall treat in our second run-through. The alchemists are following the light carried by anima mundi, or spirit in nature, who appears in Keys 17 and 21 as The Star, respectively, and The World. By placing her light within The Hermit's own lantern, Waite makes the Hermit a light unto himself. Such a star of light, so placed, signifies the aspiration of the material plane for the spiritual, and the descent of the spiritual to the material. And this completes the numerical cycle that was initiated by the Magician's "above/below" gesture, with the two planes now conjoined within one lantern.
Roberts' explanation of Waite's source seems sound. The image Roberts reproduces comes from the bottom panel of the frontispiece/title page of the Musæum Hermeticum, an image created by Matthaus Merian. It appears in both the 1625 and the expanded 1678 editions, and in some of the English translations.
Merian's image is itself derived from an earlier alchemical text, Michael Maier's 1617 emblem book Atalanta Fugiens. Maier's emblem #42 (below) shows an Alchemist tracking Nature, his Guide. He follows her footsteps, using his staff (Reason), glasses (Experience), and lantern (Reading).
Giornale Nuovo points out that this emblem is notably different from most of the rest of Maier's images.
[Emblem #42], for example, appears to have been Maier’s own invention: de Jong, at least, was unable to find antecedents for it in the alchemical literature. The accompanying motto reads ‘May Nature, Reason, Exercise and Literature be the guide, staff, spectacles and lamp for him who participates in chemistry.’ Nature here is portrayed as the woman bearing fruit & flowers, and Reason is the pilgrim’s staff, Experience his spectacles, and Literature his light. Frankly, it is a relief to find symbolism so straightforward, amid all this esoterica.
It was derivative, but not from alchemical literature. It comes from Alciato himself, the creator of the emblem-book tradition. First, note that in both the Atalanta Fugiens and Musaeum Hermeticum images we have an alchemist (Hermeticist) following a woman (Nature), and in both cases the woman displays conventional attributes of Fortuna: a sail and a cornucopia. Alciato had Hermes and Fortuna together in a similar manner. The subject matter is closely related. Alciato says:
As Fortune rests on a sphere, so Hermes sits on a cube. He presides over the arts, she over the varied chances of life. Art was developed to counteract the effect of Fortune, but when Fortune is bad it often needs the assistance of Art. Therefore, studious youths, learn good arts, which bring with them the benefits of an outcome not subject to chance.
That is, Art improves upon Nature. Maier's Alchemist, indeed, all alchemists, attempt to do something natural by artificial means, to speed up or otherwise enhance natural processes. Maier says:
Nature presupposes Natural Bodies; and Spirits as the Subjects; first ministered by Nature, upon which Art may afterwards exert itself by Preparing, Purifying, and rendering them Capable of having that produced from them, which Art proposes for its end. So the Potter takes Earth and Water; the Glassmaker ashes and Sand; a Smith Iron, Brass, Lead, Tin, Copper, Silver and Gold; a Tanner raw Hides; and so other Artists take other things. The Chemist has regard to his Materials; theirs are known to them the very first day, but when he Begins, his are utterly unknown to him for many years, and perhaps for his whole life. Nature does indeed lay its finger upon the matters; but there are many things which obscure the impression of Nature, that it cannot be known. Therefore the first intention must be TO intimately contemplate Nature and to see how she proceeds in her operations, to this end that the natural Subjects of Chemistry, without defect or superfluity may be attained to. From whence let Nature be thy guide and companion of so great a journey, and follow her footsteps.
Roberts is certainly correct that Waite's use of the Star of David as the Hermit's light was based on Merian's image. That design was clearly a revision of Maier's image, which did not itself have the element in question. Only the most proximate source included the six-pointed star. Maier's Fortuna, the intermediate source, is clearly related both formally and semantically to Merian's many-breasted Natura figure. It is fascinating to note that Maier was probably inspired by Hermes and Fortuna in Alciato's original emblem, but also completely irrelevant to the initial question.
Significant changes were made at each step of the process. Each borrowing was understandable but partial, and each revision added things as well. This is the way artists have always tended to use their sources of inspiration. There may be even more potential influences to be considered, and the possibility of overdetermination. For example, here are Bob O'Neill's comments about the star in the lantern of Waite's Hermit card.
The hexagon appears on the magic lantern illustrated by Levi (Transcendental Magic, p 252). In The Secret Tradition in Freemasonry (p 36), Waite shows a similar symbol, a radiant hexagon which he describes as “The Hexagon, encompassed by a solar glory.” The Frontispiece in Waite’s Hermetic Museum shows the hermit following the bright hexagonal light being carried before him by a female spirit. A further hint may be offered in Waite’s poem: “At the End of Things” from The Collected Poems of Arthur Edward Waite. The poem describes a spiritual pilgrim:
And a star I stole for the good of my soul,
Lest the darkness came down on my sins...
I carried the star; that star led me...
Did my star more than the cozening guide?
The fool, as I think, at the chasm's brink...
Did, even as I, in the end rejoice.
The card suggests that the Hermit is now holding the star aloft so that others may find it. For example, in Lamps of Western Mysticism (p 307), we find “I put up this Lamp of the Heights as a beacon for others hereafter.”
This too is interesting, and tangentially relevant, but far more speculative and far less explanatory. The proximate source for the lantern carried by Waite's Hermit was the book which he translated. The other details of the story may be interesting, but in terms of explaining the symbolism they are “surplus to requirements”.