Basques and Jews would certainly not be considered races. While these groups are sufficiently different from other Caucasoids, they are certainly not so different that individual Basques or Jews could be identified via a genetic test. So far, I have not seen that happen, nor do I expect it to happen soon.

It might happen in the future. Consider the following scenario. Each individual's complete genome is recorded, along with its holder's ethnic effiliation. Then, the simple objective test that takes an individual (e.g., Avi) and an ethnic affiliation (e.g., Jewish) and outputs a positive result if Avi's genome is marked as 'Jewish' in the database meets criteria #1-2. In this case the "pattern" that Jews share is the set of all extand Jewish genomes.

But there are problems! Because any offspring of two Jews will represent an entirely new (and unrecorded) genome, hence it will not meet criterion #3. This is an extreme case used to illustrate the following point: You can make a very specific test to identify members of any given population. But, the more specific the test is, the harder it is to ensure that the pattern will repeat in the next generation.

I won't comment on Mestizos at the present time, since I'm still working on the application of the definition on mixed populations.

The population is defined in any way one wants. No matter how it is defined, it must be shown to pass a test. Of course, the easiest way to define it is: all the people who pass the test. Then, by definition conditions #1,2 are met.

"Geographic races" are an obvious application of the race concept. But, it may not be the only one. Geographic adaptations as well as random drift in each population will result in distinct allele frequencies in between two populations, to an extent that the probability that the two populations may produce the same kind of individual will be minimized.

But, classification always depends on the part of the genome you are looking at. There are alleles that have east-west clines, and alleles that have north-south clines, alleles that may have mountain-plains clines, or social clines, etc. Thus, it may be possible to describe a pattern (for some part of the genome) found in members of a population group that is not defined geographically.

I am fully prepared to call such a group a race, inasmuch as it possesses a set of traits that it can reproduce and which are lost by inter-racial mating.

I personally doubt that such races will be found, or that they will be interesting. The main reason for this is that, unless one assumes very intense assortative mating (e.g., in a hypothetical 'race' of blacksmiths that reproduces among its own and has specific adaptations for metallurgy), at each generation a fraction of the members of such a race will breed with the general population (by definition thus losing their racial pattern), and over a few generations will go extinct.

In contrast, geographic races have not faced that problem for thousands of years, that is why their founding populations became races in the first place: e.g., people with an emergent 'Mongoloid' racial pattern just had to assortatively mate with members of their own population for a very long time. That is what allowed them to finally become distinct.