The other interesting result would be if the expected neutrino type was not detected by this experiment, invalidating the hypothesis. This would raise further questions such as: is there some other mechanism powering the Sun? Is there something deficient in our understanding of neutrinos that prevented us from detecting them despite them being there?
That almost happened, in the early days of neutrino dectection - before things like old mines full of purified water and 3-D arrays of photodetectors running for months at a time, and you could count the number of detected neutrinos on two hands (in bi-quinary so you could go a bit higher than ten). This was when the detectors could only detect the type of neutrino directly generated by fusion reactions, and before the discovery of neutrino oscillation, when it wasn't yet clear whether neutrinos had no, or very very little, rest mass.
Early numbers, and their error bounds, made it clear that there weren't enough neutrinos being detected. (This was known for years as the "missing neutrino problem".) But the earliest ones WERE about right for a situation where all the stars EXCEPT the sun were running by fusion and the sun was out.
That may sound odd. But there was a very cute explanation that made it plausible:
The gradual gravitatonal collapse of the sun, as heat is radiated away, could power it for millenia. It's nowhere near enough to power it long enough to explain the fossil record, but it IS enough to have kept it running for historic time. Meanwhile, if a fusion reaction were to start up near the center of such a ball of collapsing gas, it would also take many years for the heat to make it to the surface. Neutrinos (which go through the sun like marbles through a light mist) are about the only signature of what's going on in there NOW.
But suppose, instead of fusing continuously, stars were reciprocating engines. They might run without fusion for centuries, or millenia, until they were compressed enough to "light up" at the center. Then the fusion heat and reaction products might make the reaction ramp up. They'd burn for a little while (which would heat them up and expand them mabye a few inches), until the decreased density and/or reduction in fuel and/or accumulation of reaction products "put the fire out" again. Repeat for the life of the star.
In this scenario, if our sun happened to be between "putts (and the very nearest stars didn't happen to have an unusual distribution of where they were in their cycles), you'd see the same neutrio flux from the rest of the sky as if all the rest of the stars were running continuous fusion. That's because it's the average of stars that are "on" and "off", and comes out to the same amount of total fusion and neutrinos.
Of course later data, both larger samples and detectors that could "see" the other neutrino types, put the kibosh on that model. A big part of it was the discovery of neutrino oscillations, allowing a stream of neutrinos that started out as one type in the sun to arrive as a mix of the three types. (This means that neutrinos have a non-zero rest mass, fly slightly slower than light, and thus experience time and are ABLE to change from one type to another.)
A pitty, thugh. By the time this was discovered I had done an outline for a five-volume fiction cycle, working through at least four genres, based on the sun going "putt" from time to time. B-b