So my mom's second cousin's test completed, and I was looking forward to comparing both of them against their common cousin (one generation down, 2x1r). Interestingly, comparing the DNA of mom to the 2nd cousin is an almost completely disjoint set relative to the 2x1r:

And, yes, the 2x1r shows up as expected as a relative of the 2nd cousin.

This, I guess, is why you test as many family members as you can.