This seems to be causing huge confusion - it may be helpful to understand how "dual illuminants" are actually used in processing:
In concept, processing from camera to finished image is in two steps:
Step 1: Convert from sensor readings (aka raw data) to "absolute" color values, in principle in an XY-type space. Critical point is that these are "absolute" values; they depend on the actual color of the light - the wavelength. So in the situation where you shine a tungsten light on a white sheet of paper, what you're measuring is the color of the tungsten light, not that the sheet of paper is white.
Step 2: Convert the absolute (XY) light values to something humans recognize - this is the white balance step, taking into account the fact that the light was tungsten, and adjusting the color of the sheet of paper in the final image to be white, white being what we see.
Dual illuminates are ONLY used in step 1 - they're just a way of better interpreting what the raw data converts to in XY type values. Dual illuminants play no role in step 2. They might give you a slightly better white balance, but that's only because they delivered a better measure of what the light reflected off various parts of the scene was, not because they're playing any role in white balance process.
Put another way, if the sensor in your camera was perfect, dual illuminants would make no difference at all. What they do is allow the software to better estimate what the scene actually looked like from what an imperfect sensor measured.
The reason why Adobe recommends D65 as an end-stop is probably just because that's where color temperatures pretty much cease to make sense as a practical photographic measure. Anything "more blue" is likely not a continuous spectrum light source.
Here's what I'd recommend:
1. For scenes lit by something with a continuous spectrum (daylight, tungsten lights), dual illuminant profiles make good sense, basically because color temperature makes sense for those lights.
2. For lights that don't have approximately continuous spectrums (sodium vapor, some fluorescents, etc) dual illuminant profiles won't really help, because color temperature starts to be fairly useless in isolation - to get a good while balance, you're going to need tint as well. So if the image is important, create a single illuminant profile with that light source.
Finally, bear in mind that dual illuminant profiles are just an optimization - so far as I am aware, no other camera company/raw developer has found the improvement compelling enough to adopt the idea.