We observe the direct excitation of pairs of Cs atoms from the ground state to molecular states correlating asymptotically to nsn'f asymptotes. The molecular resonances are interpreted as originating from the dipole-quadrupole interaction between the nsn'f pair states and close-by npnp asymptotes (22≤n≤32). This interpretation is supported by Stark spectroscopy of the pair states and a detailed modeling of the interaction potentials. The dipole-quadrupole interaction mixes electronic states of opposite parity and, thus, requires a coupling between electronic and nuclear motion to conserve the total parity of the system. This non-Born-Oppenheimer coupling is facilitated by the near-degeneracy of even- and odd-L partial waves in the atom-atom scattering which have opposite parity.