  Excited states in the $T_z = 0, -1$ nuclei $^{62}$Ga and $^{62}$Ge were
populated in direct reactions of relativistic radioactive ion beams at the
RIBF. Coincident \grays were measured with the DALI2$^+$ array and uniquely
assigned to the $A=62$ isobars. In addition, $^{62}$Ge was also studied
independently at JYFL-ACCLAB using the ${}^{24}$Mg(${}^{40}$Ca,$2n$)${}^{62}$Ge
fusion-evaporation reaction. The first excited $T=1, J^\pi =2^+$ states in
$^{62}$Ga and $^{62}$Ge were identified at $979(1)$ and $965(1)$~keV,
respectively, resolving discrepant interpretations in the literature. States
beyond the first $2^+$ state in $^{62}$Ge were also identified for the first
time in the present work. The results are compared with shell-model
calculations in the $fp$ model space. Mirror and triplet energy differences are
analyzed in terms of individual charge-symmetry and charge-independence
breaking contributions. The MED results confirm the shrinkage of the
$p$-orbits' radii when they are occupied by at least one nucleon on average.
