Even if it is "just a synonym", it does not imply that we should shift terminology. Terminology is not just about definition (denotation), it is also about implication (connotation).

As others have pointed out, "mechanistic" and "reductionist" have unwanted connotations, while "gears-level" has only the connotations the community gives it... along with the intuitive implication that it's a model that is specific enough that you could build it, that you would need to know what gears exist and how they connect. (In contrast, it's much easier to say that a model is mechanistic or reductionist, without it actually being, well, gears-level!)

Between the lack of pre-existing negative connotations and the intuition pump, there seems to me to be more than enough value to use the term in preference over the other words, even if it were an exact synonym!

I for one don't plan on using "mechanistic" where I currently talk about "gears-like" simply because I know what intuition the latter is pointing at but I'm much less sure about the former. Maybe down the road they'll turn out to be equivalent. But I'll need to see that, and why, before it'll feel-make sense for me to switch. Sort of like needing to see and grok a math proof that two things are equivalent before I feel comfortable using that fact.

Not that I determine how Less Wrong does or doesn't use this terminology. I'm just being honest about my intentions here.

A minor aside: To me, "gears-level" doesn't actually make sense. I think I used to use that phrasing, but it now strikes me as an incoherent metaphor. Level of what? Level of detail of the model? You can add a ton of detail to a model without affecting how gears-like it is. I think it's self-referential in roughly the style of "This quoted sentence talks about itself." I think it's intuitively pointing at how gears-like a model is, and on the scale of "not very many gears at all" to "absolutely transparently made of gears", it's on a level where we can talk about how the gears interact.

That said, there is a context in which I'd use a similar phrase and I think it makes perfect sense. "Can we discuss this model at the gears level?" That feels to me like we're talking about a very gears-like model already but we aren't yet examining the gears.

I interpret the opening question being about whether the property of being visibly made of gears is the same as "mechanistic". I think that's quite plausible, given that "mechanistic" means "like a mechanism", which is a metaphor pointing at quite literally a clockwork machine made of literal physical gears. The same intuition seems to have inspired both of them.

But as I said, I await the proof.

There's a tag for gears level and in the original post it looks like everyone in the comments was confused even then what gears-level meant, and in particular there were a lot of non-overlapping definitions given. In particular, the author, Valentine, also expresses confusion.

The definition given, however, is:

1. Does the model pay rent? If it does, and if it were falsified, how much (and how precisely) could you infer other things from the falsification?

 2. How incoherent is it to imagine that the model is accurate but that a given variable could be different?

 3. If you knew the model were accurate but you were to forget the value of one variable, could you rederive it?

I'm not convinced that how people have been using it in more recent posts though. I think the one upside is that "gears-level" is probably easier to teach than "reductionist" but contingent on someone knowing the word "reductionism" it is clearly simpler to just use that word. In the history of the tag, there was also previously "See also: Reductionism" with a link.

In the original post, I think Valentine was trying to get at something complex/not fully encapsulated by an existing word or short phrase, but it's not clear to me that it was well communicated to others. I would be down for tabooing "gears-level" as a (general) term on lesswrong. I can't think of an instance after the original where someone used the term "gears-level" to not mean something more specific, like "mechanistic" or "reductionist."

That said, given I don't think I really understand what was meant by "gears-level' in the original, when there are suitable replacements, I would ideally like to hear from someone who thinks they do. In particular, like Valentine or brook. If there were no objections maybe clean-up the tag by removing it and/or linking to other related terms.

Both of these would be clearer if replaced by "causal". That is what they are both talking about: causes and effects.

I think the best pointer for gears-level as it is used nowadays is John Wentworth's post Gears vs Behavior. And in this summary comment, he explicitly says that the definition is the opposite of a black box, and that gears-level vs black box is a binary distinction.

Gears-level models are the opposite of black-box models.

[...]

One important corollary to this (from a related comment): gears/no gears is a binary distinction, not a sliding scale.

As for the original question, I feel that "mechanistic" can be applied to models that are just one neat equation but with no moving parts, such that you don't know how to alter the equation when the underlying causal process.

If mechanistic indeed means the opposite of black-box, then in principle we could replace gears-level model.

Isn't mechanistic specifically about physical properties? Could you say that an explanation of a social phenomenon is "mechanistic", even though it makes zero references to physical reality?

Normally and one might be tempted to generalise that usually when you know some thing you know the surrounfing "topic". However there are cases when this is lacking. There are such things as zero-knowledge proofs. Also any reductio ad absurdum (assuume not p. Derive q and not q from not p. Therefore p) is going to be very silent about small alterations to the claims.

Also dismissing perpetual motions machines because you believe energy is conserved will make no particular claim on what is the issue with this particular scheme. This can be rigorous and robust which might be alot what people often shoot for with "mechanistic" but it is general and fails to be particular and thus not gear-level (it kind of concretely doesn't care whether the machine in question even has gears or not).

White box or transparent box model, as opposed to a black box model.