Hi Andrew, The moment I saw "Sancai" mentioned as the subject I thought the post might be from you. :-) I don't know much about Tang Sancai, but tell you what I know. The majority of Tang Sancai was made of low-fired white clay, but there seem to exist some with red clay also. Why that is I do not know, but usually that would have been due to availability near the kiln(s). They must have been fired in different places. Apart from that, I know only that in the Tang dynasty Sancai wares were used exclusively as burial items; the ceramics used in everyday life at the time were quite different. I was told that some look like new when excavated, if they have been undisturbed over the more than a thousand years that passed since.
What that document at the link you provided mentions is the spectrometric analysis, it seems. I have on this in the lower half of this page: https://www.chinese-antique-porcelain.com/scientific-authentication.html
Whether the origin can be located exactly with spectrometric analysis depends on two conditions, in my view. The first is that the comparison data available for the location(s) were sampled properly. As far as I know up to 40 element traces can be measured with this analysis method; that is a pretty high number. The higher the number of component traces in the clay the higher the exactness of the result, I would think. If archaeological data from excavations of the Tang dynasty layer prove that the composition of the shards correspond to the clay composition in the surroundings (mining area), it is probably fairly sure that the items/shards were produced in the area and not elsewhere.
The second condition would of course be that no second or third kiln sites anywhere would have a clay composition that is very similar.
While the fakers seem to be trying to falsify the results by adding the required material traces to the clay in order to change its composition, following proper procedures when assembling the standard comparison data should make it possible to obtain a fairly exact result (if condition two isn't rendering it void).
If reliable comparison data are available, then the result will likely be exact. I see the problem more with commercial fakers who will try to fool the instruments by faking the clay composition. But, if that can be excluded...
If you make a Google image search with this "唐三彩" you should get dozens of images of Tang Sancai items (including fake ones), but it should give a general overview of what exists, and the colors. Mostly figurines and decorative items, plates and bowls are few, because the wares were only for the tombs.