Hume's Treatise 1.2.6, "Of the Idea of Existence, and External Existence", is easily overlooked, but raises some important questions. In discussing the idea of existence, or being, Hume gives an interesting argument, which could be formulated in something like the following way:
(1) Whatever is conceived in consciousness or memory is conceived as existent.
(2) The idea of existence is derived from this conception of things as existent in consciousness or memory.
(3) Every idea derives from a similar impression.
(4) Either the idea of existence is derived from a distinct impression conjoined to every perception or object, or the idea of existence is the same as the idea of each perception or object.
(5) No two distinct impressions are inseparably conjoined.
(6) Therefore the idea of existence is the same as any idea of each perception or object.
Hume also considers a possible proposal for a third option: perhaps the distinction is a distinction of reason, so that the idea of existence is neither strictly different nor strictly separate from each 'perception or object'. In Hume's account of distinctions of reason, we actually only have one idea but we compare it to different sets of similar ideas. For instance, figure and color are found in the same empirical ideas -- you can't have figure without color or color without figure. Since Hume accepts Berkeley's argument against abstract ideas, there is no literal 'idea of figure' and 'idea of color'. But if we have the idea of a black triangle, we can compare it either to ideas of other black things or to ideas of other triangular things. This won't work for existence or being, however, because by (1), we can't compare any idea to other ideas that are not conceived as existent.
The point about the distinction of reason goes quickly, but I think it's quite important, since in his argument Hume is effectively assuming a principle that the idea of being applies univocally to everything. The argument wouldn't work if there were different but related ideas of being, because then we could get the comparisons required for distinctions of reason.
This univocity of being, however, has an interesting implication; since the existence that Hume identifies is the existence we are considering whenever we think of anything and can say that in some sense we are conceiving it as existent. This is what is historically known as intentional being, or cognitional being, or objective being, depending on the context -- being in the mind, or being perceived. Since our idea of being is derived from this (Hume is very clear about this with (2)), and since Hume assumes the univocity of being, 'being' and 'being in the mind' (in the common sense of the latter phrase) would be synonymous for Hume. All being is intentional being; Hume is committed to Berkeley's idea that esse est percipi, allowing of course for some differences in how they think of perception.
Thus a number of important metaphysical questions are coming together in this little argument. (1) gives us intentional being; (2) guarantees the univocity of being that we have mentioned; (3) is the copy principle that is the foundation of Humean empiricism; the dilemma in (4) presupposes Hume's rejection of abstract ideas, which is the foundation of his account of distinctions of reason; (5) is the second most important principle of Humean empricism, the separability principle. Since (2) through (5) are all key principles of early modern empiricism, Hume does seem right that the conclusion is one that would have to be accepted by any such empiricist.
Of course, (1) is correct (which gives us intentional being), but there are excellent reasons to reject each of (2) through (5).