The mirror is reflecting the sun, so if the sun were really emanating from the direction of the mirror, I'd expect it to flare just as it would if looking directly. The angular size of the mirror at these terrestrial distances is just a small fraction of the 0.55° diameter of the sun, so it's only able to reflect a portion. However, even that small portion is bright enough to "flare" beyond the 7" mirror boundaries.
I have another larger circular mirror I will turn into a signal mirror (with reflective tape and a sighting hole) and hope to try that too to compare. I imagine it will produce an even larger flare. The rectangular mirror the F.R.E.E. group used would be larger still, but I don't think it's necessary. The objective is to make positive identification of the location of the signaler. If using an ever-larger mirror is required, then that must mean something is happening optically that is distinguishable from the earth being flat. I also don't want to be toting that large of a mirror around, and I also want a mirror that I can positively target and not just wiggle around.
If the size of the mirror turns out to matter, then that can be part of the analysis.
I'm not sure how much the intervening atmosphere contributes to the bloom in size of the light. One of the globe earth responding videos suggested that the moisture in the air near the surface of the water helped make the light appear above the physical curved horizon, as if the aerosols along the light path were retransmitting the light. I don't know if I buy that, but they do have an interesting demonstration of how a light source hidden behind a cylinder has it's light become visible when aerosol particulates are created in the intervening space. I linked to that video earlier in this thread, but I really don't think that's what's happening in the Monterey video. We're not just seeing a diffused light but you can make out the actual rectangular shape of the mirror.
My feeling is that it's a strongly refractive mass of air close to the surface, almost like a surface duct. I'm in the uncomfortable spot of maybe taking Tom's "compression" explanation and using it to explain how, maybe, 20-30 feet from the water surface up is being compressed into a thin band, not producing a mirage (superior mirage) but to cause a looming effect. The air near the surface of the water would have to be quite dense, meaning it would be quite cooler than the rarer air just tens or maybe a hundred feet above. I don't know what the sea and air temp were that day or what the humidity/dew point was, so it's hard to tell. All I can do is speculate.
Which is why I think it's important to see if their results are repeatable. And not just once, but on different days. And maybe at different locations. I mentioned before hoping to participate in their return to the Salton Sea in February where they plan on using this technique there, and over greater distances. I think with both globe and flat earthers working together, the exercise will be less likely to be conducted in a way to confirm a bias. We'll both be able to balance each others tendencies to try to produce results we might want.
I've rambled off the point, so getting back to the mirror type/size, for this first round, I intend to stick with my mirror configuration for both the 12.9 mile and then the 20+ mile tests. And I will be paying close attention to and recording sea and air temperature and other meteorological conditions, including the ozone/air quality indices since this pesky "haze" is unpredictable and may be a difference factor between my results and those from Monterey.
I'm still hoping for an opportunity to get to Monterey myself sometime after the New Year, though my focus then will be on the Bishop Experiment recreation. However, this mirror technique might come in handy for that too. I just would need to enlist a volunteer to drive around to Santa Cruz. I may not have the time for that and will just have to rely on visual identification of Santa Cruz shoreline landmarks.