[...] it is liable to the same difficulties; and is over-and-above loaded with this absurdity, that it at once denies and establishes the vulgar supposition. Philosophers deny our resembling perceptions to be identically the same, and uninterrupted; and yet have so great a propensity to believe them such, that they arbitrarily invent a new set of perceptions, to which they attribute these qualities.
Does this make Hume an eliminativist, or a reductionist? I have argued elsewhere that the distinction is arbitrary, and I shall argue that this applies to Hume's position also. If we define 'material object' as something which is mind-independent and permanent, then it is clear Hume is denying the existence of any such things. The only objects we are aware of, he says, are these fleeting and perishable sense-impressions, which have no continued and uninterrupted existence. So he is an eliminativist regarding material objects defined in this way. But as I have argued, we don't have adopt this definition. If we define 'material object' as something identical with our sense-impression, then uninterrupted existence turns into a mere accidental feature of objects. An accidental feature that, as Hume argues, may not apply to any object at all, just as 'carried by the ether' does not apply to light, as people once thought.
In summary: whether Hume is an eliminativist or reductionist about the term 'material object' depends entirely on how you choose to define the term. There are the observable phenomena - the sense impressions - and there is whatever unobservable X explains or underlies these phenomena. And that X can have any features you like. There are no 'essential features' of things that are essentially unobservable.
* A Treatise of Human Nature, Book I. 4. ii - "Of scepticism with regard to the senses". This section is essential reading for any understanding of Hume. People often don't read it because it occurs towards the end of the first book, and because there is a lot of focus on the causation stuff in Part III. Part IV, particularly sections 2-4, are by far the most interesting and enjoyable and indeed strange parts of the work.