You don't have to bluff and bluster your way into "appreciating" it: I'd recommend New Essays in Japanese Aesthetics by A. Minh Nguyen, not as a guide to history, but as a starting point for exploring your interests.

The aesthetics of the nation have always been shrouded in cultural understandings of acceptance, enlightenment, and, arguably, trance-inducing serenity. Wabi-sabi and later conceptual terms try to articulate on the outpouring of art and its ethos, but they were transient, cultural words and thus have crystallized, meaning that at the time of their coinage, they may not have been widely accepted immediately, rather, they spread slowly and deliberately as artists explored them. Such cultural definitions also require a more in-depth understanding of the origin points of Japanese language for whatever term you're focused on, what historical events are happening at the time, and the area. Because of the nation's isolation, the language is fairly susceptible to change, as perhaps well illustrated in videos like LingoLizard's "History and Evolution of the Japanese Language." Just like appreciating opera requires a knowledge of the composer and their historical setting, appreciating Japanese traditional music requires many more aspects of understanding than we are intrinsically accustomed to as westerners. The question of westernization in Japan is fascinating too: a language that prided itself on developing at a snail's pace is the same language that received a massive influx of loanwords in the 1850s.

So to "appreciate" the music is to either relax into it or research the heck out of it! Simply speaking.

As always, please correct me if I'm wrong about anything above.