One thing that I disagree with in your analysis is that one boxers care about dispositions whereas two boxers care about decisions. I think it's actually the opposite.
I myself am a fairly confident one boxer who feels the force of two boxing reasoning. I work at a trading firm and found that my firm seems to attract people who think like two boxers. I found a highly intelligent coworker (who seems to be even more intelligent than I am) who is a staunch two-boxer. He seems to understand every point I have brought up, and he brings up fair points.
During our debate, it became apparent that he assumed that, since you can't change who you were at scan time, and since the prediction (and hence money in the opaque box) follows from who you were at scan time, that the opaque box has already been filled or not, so you might as well make an extra thousand bucks since you can no longer take any action to affect the contents of the opaque box in any way.
I countered by saying that the predictor is not predicting your disposition. It is predicting your output to the decision problem. Imagine that you have to press one of two buttons to make your decision to Newcomb's problem (and that pressing both simultaneously corresponds to two-boxing). Also imagine that the population of people who get predicted suffer from involuntary muscle spasms that could cause them to press one or more buttons that they did not intend to press. Say that even in cases where the button press stemmed from an involuntary muscle spasm, the predictor is still overwhelmingly accurate. (This could definitely happen if the proclivity and direction of the muscle spasm is foreseeable at prediction time.)
In this world of involuntary decisions, the predictor is still predicting the decision itself. You could think like a two boxer all you want, but if you somehow involuntarily one box anyway, the predictor would have predicted that, and you would reap the rewards of a one boxer despite having the disposition of a two boxer.
We can extend this muscle spasm argument to the normal world, too. The predictor is predicting what you actually decide. Nothing less, nothing more. You could have the disposition of a two boxer all you want, but if you somehow one boxed anyway, you would be a one boxer (by definition).
You may not be able to control your disposition at scan time, but what actually matters is what you actually decide. The predictor's only goal is to predict your decision.
The two boxer has to be convinced that your decision follows from your disposition in order to conclude that it's worthless to one box. The one boxer says that it doesn't matter what you think, if you one box, you reap the rewards of a one boxer, regardless of how you got there.
One of the things you mention is that the signal should not be possible to fake by a bad actor (i.e.: someone who is not curious but wants to act curious to create plausible deniability).
Most responses here seem to be attacking this question from the perspective of modeling curiosity. Instead, let's focus on use cases of feigning curiosity, and see if we can reason about what a bad actor may be incapable of doing.
Think about the disposition of someone whose intent is to embarrass rather than to learn. Such a person wants to assert dominance. He wants to win and show that he is superior. To gain status at your expense. He is calloused to his effect on your emotions.
In real life, mirroring shows empathy. Empathy is incompatible with this persona. Thus, mirroring is a good signal. In posts, mirroring can happen with adopting similar jargon.
Another thread here is the idea of coming out on top. If you can elevate the other person's status and diminish your own, this is also incompatible with the persona of asking for the purpose of asserting dominance. There are many ways to do this. For example, I recently had an experience where I was asking a successful startup investor (who has been named in the Forbes's Midas Touch list) for insight into what fueled his ambitions and risk-taking appetite. To increase the probability with which my question would be taken non-combatively, I related to him by saying, "when I was in college, I certainly wasn't focused on building my own business - heck, it hadn't even crossed my mind to do anything but study as hard as I could. And you somehow are one of the rare cases that managed to still graduate from a tough university while still successfully conducting your own businesses. How did you even get the resolve to go so above and beyond the ordinary levels of effort during a time where expectations are pretty set in stone?"
Finally, if your goal is to embarrass, and instead you end up embarrassing yourself, this also is incompatible with the disposition of someone whose goal is to embarrass. I don't know of any examples of this off the top of my head, and I fear taking this approach - perhaps because I do indeed like to maintain some level of perceived respect. This is not something I am usually able to do. But it does seem possible to skillfully embarrass yourself, but not too much, in order to signal that your goal is not to embarrass the other.
Love this! Great examples to illustrate that your identity as a one boxer is rooted in your behavior instead of your mind. And pretty cool to think this mirrors theological debates that have gone on for so long