We present new data for the transverse target asymmetry T and the very first data for the beam-target asymmetry F in the $vec gamma vec ptoeta p$ 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.
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