>I’m trying to question the coherence of the proposition itself, and not trying to refute an argument in favor of it.

The point is that just because you can't prove something to yourself it doesn't make the belief incoherent. And you can use your other tools to arrive at likelihoods for said belief.

At any rate, there's plenty of things we believe about say quantum mechanics without being able to observe them directly by using theory and observing secondary effects.

In theory it's also possible to eventually have an exact definition of what we mean by consciousness, figure out which parts of the brain are relevant in what ways and observe secondary effects and use theory to confirm others have it same as with QM. It's all caused by physical effects and at a higher level than things we already reason about just fine.