It uses 4.5" thermal paper - with multiple Agilent catalogue numbers, but the most common was 5080-8800, and you will find plenty of suppliers, as other toys ( the HP85 computer ? ) also used it.
Obviously, no ink is required. But two things to watch for. The print heads die, usually one of the segments. That's OK if it's part of the text, but hopeless if it's the chromatogram.
The second is that the rubber on the print head belt, and feet, turns to goo after some time ( ten - twenty years ), and then there are no teeth, as they have remainly on the drive sprocket - whith spins happily. I have used a long serrated edge cable tie as belt, but it's not agood option...
The difficulty will be getting any hardware spares - such as the printhead, but the optional battery packs can easily be rebuilt by any of the firms offering power tool battery rebuilds.
The family were offen referred to as HP339X, so a search on that or 3390 should help locate suppliers.
However, the problem may be that you can't easily reprocess data with these integrators, so you may need to push the output to a computer with a software package for reintegration, which rather defeats the purpose..
I think they are ideal for simple, routine uses, but once you want to do anything adventurous with the data, the 3392 will soon be very frustrating....
Please keep having fun,
Bruce Hamilton