What observables are indicative of BCS Cooper pair condensation? What observables are indicative of BCS Cooper pair condensation?
"Thought" experiments and "numerical" experiments are allowed.
This question is motivated by the question Has BCS Cooper pair condensate been observed in experiment? ,
and by our recent research on anyon superfluidity where anyons are emergent from a fermion system.
"BCS Cooper pair condensation" has a formal theoretical description. Here I am looking for an experiemental or numerical definition of "BCS Cooper pair condensation".
 A: This question is indeed a little bit on the philosophical side (or perhaps this answer is!)
It is much easier (and probably scientifically more accurate) to state when a system is not BCS Cooper-paired than to say when it is. We can say that we have evidence that a material is a BCS-type superconductor, but we cannot say it is one with 100% certainty. BCS is a model and of course in any real material there will be deviations due to band-structure, electron-electron interactions, etc.
There are numerous experiments that are indicative of and consistent with the BCS theory of superconductivity. Of course, the most notable is the Hebel-Slichter peak, which BCS predicted. Then there are the Giaver tunneling experiments which showed a uniform (s-wave) gap in the density of states. There are also the phonon bumps in the second derivative of tunneling spectra analyzed in depth by McMillan that are suggestive of a phonon mechanism. Then there are the experiments with flux quantization and Josephson tunneling which show charge $2e$ quasiparticles. Of course this latter example is also present in unconventional superconductors. However, these are all suggestive of BCS-type condensation when considered as a whole.
I do believe this question is in some sense ill-posed because all of these experimental signatures, which are predicted by BCS are not necessarily specific to BCS.
Most unconventional superconductors don't conform to the BCS theory because they violate one or several prerequisites for a BCS superconductor such as:
1) Arising from a Fermi Liquid normal state
2) Being three-dimensional metals prior to undergoing the superconducting transition
3) Being adversely affected by magnetic impurities
4) Being unaffected by non-magnetic impurities
5) Being phonon-driven
6) A few others
Nature is much cleverer than us humans and it is easy to imagine her coming up with much more exotic mechanisms of superconductivity that conform to almost all but a single glaring absence of an experimental signature that we thought necessary for Cooper pairing or condensation to occur.
We should therefore not ask if a specific superconductor is a BCS superconductor but examine whether or not we can find evidence to show that it is not a BCS superconductor. If the superconductor in question keeps passing the tests, the closer we are to certainty that it is a BCS-type mechanism that is responsible for the superconductivity in the particular material.
A: Isn't the proximity effect a delocalization of the condensate outside the superconductor ? Then, one can probe this effect via tunnelling (density of state probe). 
Vortex are also an inhomogeneity of the condensate that one can easily visualise (STM, X-ray, ...). 
Well, any kind of inhomogeneity can be seen as I believe. But I do not know of an experiment probing the stable, constant condensate (each time, one needs phase gradient in what I know).
It may also be possible to probe the edge currents proposed by London long ago (I'm not aware of such a detection, nor of an actual experiment).
EDIT: Ok, an other way of answering, I may have misunderstood the question. After reading this topic, maybe some better answers would be: 
1) The coupling of two electrons to form a bound state, mediated by a phonon (à la Cooper / Bardeen and Schrieffer). So in principle one could generate it by phonon excitations (already done in the 70's if I remember correctly)
2) The emergence of a macroscopic quantum state from interacting electrons, and the creation of a quantum macroscopic state with all electrons sharing the same phase. So in principle one could observe the growing of the phase rigidity.
3) The emergence of a gapped excitation at the Fermi level.
But I still believe the question is not clear ... :-( 
Well, as it must at the beginning of organising minds :-) 
A: This answer, which in essence is not really mine, is intended to understand a bit better what the actual question is really about. I was opening the Feynman's book a few days ago and I remembered this question. Let's see if Feynman can help us :-)
Feynman, in his book Statistical physics - A set of lectures wrote a section entitled 10.8 - Real test of existence of pair states and energy gap which might be of interest for you.
To give you the idea developed there, let me copy a few sentences:

Any phenomenon in which scattering of electrons is involved will serve as a test for the existence of the pair states. Attenuation of phonons and paramagnetic relaxation are examples. […]
When the pair states proposed in the BCS theory exist, a scattering of an electron $k\uparrow$ induces an interference with the paired electron at $-k\downarrow$ […]
Let us now discuss gap experiments. [… then Feynman describes the tunnelling experiment to measure the DOS ...]

My feeling is that Feynman captures the essence of the BCS Cooper pair condensate. But it also seems to me that this is precisely this notion which is unclear.
A: It is known from the tunneling of Cooper pairs through Josephson junctions / Squids that there are excitations in superconductors that (a) have charge exactly 2 electron charges and (b) are in a condensate.  Thus, examining the oscillations in an AC Squid establishes that there are Cooper Pairs.  It does not tell us about the symmetry or similar but does show us that there are pairs.  Is this adequate to answer this question?
