One key question would be to ask them to describe the experiences they had which they believe mean they're enlightened. Anyone who tries to describe the content of their experiencein any way whatsoever, is not the real thing. Any experience with an actual description, quite likly could be valid steps along the path, but are certainly not the end. (The reason for this question is complex, but it boils down to the fact that the actual event of enlightenment is not experienced in any way, shape or form. Any description of it can only be made in terms of the approach to it, and the exit from it. These do have distinct patterns that can be recognised by someone familiar with them and are the closest things available to diagnostic criteria.)
This question will only help sort out the real deal from the honestly deluded. It will only help screen out malicious frauds to the extect of whether or not they know the correct answer. Most won't, but there are now books available that go into explicit detail, so the possibility can't be ruled out. I should note that I don't claim to be enlightened, I merely claim to have passed one of the early, but key milestones, which is generally recognised as the threshold for which you can talk about this stuff without screwing it up too much.
The only real answer to your question I can think of would be have a fully abled psychic read everyone. I've discussed before why that's theoretically possibly but not especially likely. (Side note: how would you measure the results of such a test? Given you currently don't really have a definition of what enlightenment is and what it means/represents, how you would find your test subjects and how would you group them? How would you verify my results? I can only see this test working if the person in charge of the test is also fully enlightenend and a psychic... in which case they wouldn't need to be running it, and would be unable to prove anything to the skeptics without such abilities.)
Two possible experiements I can think of would lend some credability, but really don't represent definitive proof of a whole lot.
1) Emotions affecting growth, e.g. the experiement where cooked rice is left to go off with emotions stuck on a label on the side of the container. The quantity, colour (and maybe toxicity?) of mould that grows on the rice is determined by the emotion (e.g. love or hate) on the label. It would be simple to execute this in highly controlled conditions where everything is identical except the label, which is outside the sealed container and according to standard beliefs, cannot affect the contents. The hypothesis is that emotions have an energetic resonance which affects the mould/bacteria. One difficulty would be rating the resulting growths. I suppose you could show the cultures to a large amount of test subjects and collect data to show that a statistically significant portion of subjects rated the hate mould subjectively much worse than the love mould. This has been done before on a limited scale, yet we're still here having this discussion. It doesn't prove enough (despite having no explanation to account for it) therefore it is ignored.
2) Similar to the above, freezing water labeled with emotions. This experiment is more well know, not sure if anyone has attempted to replicate. Same problems apply: subjective evaluation of the results. Again there is a definite statistical correlation, but not no attention is paid.
3a) Self selected volunteers who identify as sensitive to crystal energies bring a set of their own crystals. The volunteer is blindfolded and asked to identify the crystals via energeric feel only. (This represents a very simple form of psychic interaction. Touch is not allowed as I can identify a scary number of crystals purely by surface texture.) A robot arm (or something) is used to hold the crystals very near, but not touching. Each is held at a series of points, including over the palms of both hands and chakra points. The subject identifies which crystal is being held near them. The key problem here is that it is MUCH harder to determine what crystal it is without touching. Ignoring surface texture, touching the crystal greatly enhances the perception of its qualities. Therefor performing the experiment without touch limits the pool of subjects to much more experienced individuals. However an expert should easily score 100% on this test repeatably. Use of the subjects own crystals means they can select a set which are distinctive and meaningful to them. However you then somehow need to rule out tampering (not that I have any idea how you'd cheat.)
3b) The same except the samples are new to the subject. More objectivly 'pure', but is a harder test and therefore makes it much more challanging, raising the bar for a useful test subject even higher.
4) It is also possible to demonstrate things like slowing metabolic functions to a virtual standstill (past the point that would usually lead to death) for extended periods of time while connected to equipment, and then demonstrate not being dead/brain damanged. This would require an extreme meditation expert.
5) Similarly, it would be possible to demonstrate living off no food or water for months at a time in a sealed environment. This requires an even more extreme expert and wouldn't get past the ethics board.
6) Plenty of experiments have already been done demonstrating abnormal brain activity whilst meditating that (IIRC) is otherwise not possible. There are peer reviewed papers on this. It doesn't prove a whole lot, but regardless, the presence of absence of these types of activities could be use as one factor of genuine-ness(even if it only measures meditative skill, not the truth of any knowledge gained.)
As a skeptic, I don't deny the possibility of something that cannot be conclusively disproven
I'm talking about something that cannot be conclusively proved. Although in the course of this discussion, I've changed my stance to "cannot be proven without a high level of co-operation from exceptionally rare and talented individuals who have less than no interest in attempting to prove anything".
But on the other hand I refuse to waste time investigating something like that until someone puts something tangible on the table to back up their incredible claims. For example answering the above question and explaining why the answer works
I expect to hear this a lot. I'm hoping to find expert individuals who have had some kind of low level experiences in the past without a full expanation that I can connect the dots for. In order to get the proof you demand, it is necessary to get experts. E.g. I can imagine a lot of hard science experiments that can be done once you had some particle physicics who understood what I'm saying of their own accord sit down and design some experiments to run on the LHC.
Hard proof is not going to materialise without some series expertiese and resources. Most experts (and those who control the resources) aren't going to be interested without the proof. Catch 22. There are some who ARE doing real research with these extra spiritual principles in mind, but getting a fair hearing from mainstream is another challange. Some good examples are Nassim Harmein and David La Point.
Harmien's work is still in progress, but he has some published papers showing very promising progress in being able to demonstrate the effects of the standard model, but with only electomagnetism and gravity. The weak and strong forces are not required, their effects are explained by a slightly different take on EM. IIRC it bridges the quantum/large scale gap by no longer requiring two sets of laws. This also begins to demonstrate the holographic nature of reality i.e. an infinite recursive fractal pattern that is the same everywhere. (I have not mentioned this yet, but it is a core part of the picture.)
La Point does not have much detail published, but has some youtube videos which seem quite promising if the results materialise. He is taking one aspect of the holographic structure and using it as an energy generator. Not free energy, but certainly something totally unlike what we currently know, that would revolutionaise the world.
There are plenty more but I'm forgetting them right now. It's way late and I've written far too much... again. (I wrote 5 pages of entirely other stuff on the trian today... this is getting out of hand, in a good way.)
I'll certainly ask around a few places to try and hunt down some more doable experiments like the first ones I mentioned above. There won't be any smoking guns, but it certainly would be good to include as many of them as possible, so thanks for the reminder.