The low-spin structure of the odd-proton nucleus ${}^{69}$Ga ($N=38$) near $N=40$ has been investigated through combined experimental and theoretical approaches. The lifetime of the first excited state $1/2^{-}$ has been measured for the first time using the $\gamma$-$\gamma$ fast-timing technique with picosecond resolution, yielding a mean lifetime of $\tau =106(8)$~ps, equivalent to a half-life of $t_{1/2}=73(6)$~ps, from which the reduced transition probabilities $B(M1)$ and $B(E2)$ for the $1/2_1^{-}\to 3/2^{-}$ (g.s.) transition have been extracted. Large-scale shell-model calculations employing the GX1APN and JUN45PN effective interactions have been performed for the odd-$A$ Ga isotopes with $N=34$ to 40 for comparison. The systematic comparison of transition strengths across the odd-$A$ Ga isotopic chain, supported by large-scale shell-model calculations, is consistent with a gradual structural change from a collectively mixed proton–neutron configuration toward a more single-particle-dominated structure as $N=40$ is approached.