I'm on 1.7.10 and the click sound is the default one.
The assets/minecraft/sounds/random/click_stereo.ogg file should be called click.ogg (without _stereo)

The main issue there is that file is also shared by clicky redstone components, and that sound was only separated in later versions. I could set it up so click.ogg is replaced in versions with the single file, so I guess the real question is whether or not making blocks also have the sound is acceptable

I personally think that's fine, as long as it sounds better than vanilla (which it does) 👍 But it's up to you. The majority of people playing on 1.7 & 1.8 aren't going to hear much redstone anyway.

Good to know the SFX is worthy then lol. Will see about adding that

So some time ago I happened across a pack someone made of just the sound, so I reached out to them to upload one for older MC, which I feel is the best solution since the dedicated file wasn't added until 1.14

Using this as an addon to the base pack accomplishes the same thing but as an optional change instead.
Link (Modrinth)

I tried that pack and they didn't rename it to click.ogg so it doesn't work.

Huh, I didn't think to check since I figured they just used the file I sent. I'll probably end up making my own page, but any more developing might be postponed for a while as I have bricked my primary monitor haha