  We report the first evidence for the $h_{b}(\text{2P}) \to
\Upsilon(\text{1S})\eta$ transition with a significance of $3.5$ standard
deviations. The decay branching fraction is measured to be
$\mathcal{B}[h_{b}(\text{2P}) \to \Upsilon(\text{1S})\eta]=(7.1 ~^{+3.7}
_{-3.2}\pm 0.8)\times10^{-3}$, which is noticeably smaller than expected. We
also set upper limits on $\pi^0$ transitions of $\mathcal{B}[h_{b}(\text{2P})
\to \Upsilon(\text{1S})\pi^0] < 1.8\times10^{-3}$, and
$\mathcal{B}[h_{b}(\text{1P})\to \Upsilon(\text{1S})\pi^0] < 1.8\times10^{-3}$,
at the $90\%$ confidence level. These results are obtained with a
$131.4$~fb$^{-1}$ data sample collected near the $\Upsilon(\text{5S})$
resonance with the Belle detector at the KEKB asymmetric-energy $e^+e^-$
collider.
