Reaching new precision frontiers in nuclear physics raises new experimental challenges as well as the demand for more sophisticated theoretical calculations. Especially in parity-violation electron scattering experiments the contribution from higher order processes, such as two-photon exchange, is comparable in size with the observed asymmetry $A_{PV}$. Hence, a precise knowledge of this contribution is mandatory to determine the systematic uncertainties. Beam-normal single spin asymmetries $A_{n}$ (or the so-called transverse asymmetries) are a direct probe of the imaginary part of the two-photon exchange amplitude in the elastic scattering of transversely polarized electrons from unpolarized nuclei. Up to now, there is significant disagreement between experiment and theory for $^{208}$Pb, which motivates more measurements to study the Q$^{2}$ and Z dependence. During a successful campaign at the MAinz MIcrotron (MAMI), using the spectrometer set-up of the A1 collaboration, the Q$^{2}$ dependence of $A_{n}$ for $^{12}$C was determined. Follow-up experiments on $^{28}$Si and $^{90}$Zr investigated the charge dependence of the transverse asymmetry and have paved the way for the future experiment on $^{208}$Pb, thus benchmarking the theoretical calculations in the heavier mass regime.