  We present new data for the transverse target asymmetry T and the very first
data for the beam-target asymmetry F in the $\vec \gamma \vec p\to\eta p$
reaction up to a center-of-mass energy of W=1.9 GeV. The data were obtained
with the Crystal-Ball/TAPS detector setup at the Glasgow tagged photon facility
of the Mainz Microtron MAMI. All existing model predictions fail to reproduce
the new data indicating a significant impact on our understanding of the
underlying dynamics of $\eta$ meson photoproduction. The peculiar nodal
structure observed in existing T data close to threshold is not confirmed.
