  We show that all GL(2, R)-equivariant point markings over orbit closures of
primitive genus two translation surfaces arise from marking pairs of points
exchanged by the hyperelliptic involution, Weierstrass points, or the golden
points in the golden eigenform locus. As corollaries, we classify the
holomorphically varying families of points over orbifold covers of genus two
Hilbert modular surfaces, solve the finite blocking problem on genus two
translation surfaces, and show that there is at most one nonarithmetic rank two
orbit closure in the minimal stratum in genus four.
