  We report on the observation and coherent excitation of atoms on the narrow
inner-shell orbital transition, connecting the erbium ground state
$[\mathrm{Xe}] 4f^{12} (^3\text{H}_6)6s^{2}$ to the excited state
$[\mathrm{Xe}] 4f^{11}(^4\text{I}_{15/2})^05d (^5\text{D}_{3/2}) 6s^{2}
(15/2,3/2)^0_7$. This transition corresponds to a wavelength of 1299 nm and is
optically closed. We perform high-resolution spectroscopy to extract the
$g_J$-factor of the $1299$-nm state and to determine the frequency shift for
four bosonic isotopes. We further demonstrate coherent control of the atomic
state and extract a lifetime of 178(19) ms which corresponds to a linewidth of
0.9(1) Hz. The experimental findings are in good agreement with our
semi-empirical model. In addition, we present theoretical calculations of the
atomic polarizability, revealing several different magic-wavelength conditions.
Finally, we make use of the vectorial polarizability and confirm a possible
magic wavelength at 532 nm.
