It seems there are a number of factors that contribute to good imaging:
1. The recording.
2. The speakers.
3. The room, its contents, and speaker/chair positioning in that room.
4. Our brain.
Within reason, most stereo recordings will give some sort of image if speakers are reasonably well set up. Our brain - psychoacoustics - seems variable in quality and experience and training can help but the phantom image appears to be a fortunate quirk of stereo listening which has no obvious evolutionary reason - does it help us survive (I think this applies to a stereo photographic image too).
What the OP is asking for is some quality/quantity that we can measure (using Room EQ Wizard for example) in our rooms, namely, once we've set up the room, speakers and listening chair as best we can.
I would have thought these measurements would be on the lines of:
1. Both speakers have exactly equal performance.
2. Some measurable qualities like phase, frequency response, direct sound and off axis response, dispersion, degree of reflections.
Before we know what these measurements are we need to understand what qualities are required, or are detrimental, to the formation of the phantom image.
One thing seems obvious - reflections are not necessary. We can get a phantom image with headphones where there are no reflections. I suspect though that reflections can damage the image, but I can't say for sure.
Another factor might be interaural crosstalk (where the left ear hears the sound not only from the left speaker but the right too). We don't get interaural crosstalk on headphones, and even if we use a processor that gives us this, or we remove it from speaker listening with ambiophonics, we still get a phantom image. It's possible these things can enhance or reduce the image - I don't know.
This article by Sean Olive from 2009 talks of desired speaker qualities:
https://seanolive.blogspot.com/2009/01/what-loudspeaker-specifications-are.html
"1.The perception of loudspeaker sound quality is dominated by linear distortions, which can be accurately quantified and predicted using a set of comprehensive anechoic frequency response measurements (see my previous posting
here)
2. Both trained and untrained listeners tend to prefer the most accurate loudspeakers when measured under controlled double-blind listening conditions (see this article
here).
3. The relationship between perception and measurement of nonlinear distortions is less well understood and needs further research. Popular specifications like Total Harmonic Distortion (THD) and Intermodulation Distortion (IM) do not accurately reflect the distortion’s audibility and effect on the perceived sound quality of the loudspeaker.
4. Current industry loudspeaker specifications are woefully inadequate in characterizing the sound quality of the loudspeaker. The commonly quoted “20 Hz - 20 kHz , +- 3 dB” single-curve specification is a good example. Floyd Toole made the observation that there is more useful performance information on the side of a tire (see tire below) compared to what’s currently found on most loudspeaker spec sheets (see Floyd's new book "
Sound Reproduction")."
The tests showed that the preference was for accurate on axis frequency response and smooth off axis with smooth phase. They also preferred some reflections. Even this is controversial as electrostats for example would measure poorly but many like them. I assume electrostats produce a phantom image so perhaps the above requirements aren't essential for our purposes, or more likely, there's something more.
I suggest it's more about speaker positioning. I know that is the case with photographic images. Take a pair of stereo images, use a stereoscope then line up the images until the stereo image appears. This can be difficult but when you hit the spot (there's just one), ships' masts come up and poke you in the eye! Perhaps stereo music is like that.
If that's the case, it is not about measurements of the speakers but exact positioning. I would think that what is needed is some recording that will produce signals coming out of the speaker which will allow us to best align the speakers. Of course some attempts (Stereophile, Chesky) have been made at this But I've never found them particularly helpful. Jim Smith in his book 'Get Better Sound' tries to help with suggestions of what you should hear on particular music CDs if your set up is right, and he is trying to produce some new product called 'Through the Sound Barrier' which may go further.