Does ginger infused honey or vodka ever go bad food-safety-wise?
Crystallized (or Stem) ginger preserved in honey is a known thing. Shelf-life is supposed to be about 3 months for the homemade kind, and I'd say twice that (at a minimum) for store bought...Those are both pretty conservative. It should have been properly prepared/canned at the start, which would reduce the possibility of some nasty microbial infestation, but obviously your mileage may vary depending on who prepared it and how it was stored.

Honey is a known reservoir of C. botulinum endospores, but C. botulinum doesn't really grow in honey (the low water activity (.6) makes it an extremely unfriendly environment for microorganisms). Honey by itself has an indefinite shelf-life. 

Vodka pickled ginger is also a known thing. Shelf-life estimates are all over the map, from three months to forever. Three months is definitely low: ginger is a tough, astringent root, and lasts three months without any particular preparation at all. Soaking it in high proof alcohol should easily multiply that.

Any alcohol of at least 80 proof in sufficient concentration should be sufficient to prohibit the growth of micro-organisms. Concentration is critical, however, and insufficient alcohol is no barrier to bacterial growth.

I'd say that 2-3 years is pushing it. And if you see anything that doesn't look normal, I'd toss it. Botulism is one of those things that you can't always detect via smell.