High-harmonic spectroscopy probes molecular dynamics using electrons liberated from the same molecule earlier in the laser cycle. It affords sub-angstrom ngstrom spatial and subfemtosecond temporal resolution. Nuclear dynamics in the intermediate cation influence the spectrum of the emitted high-harmonic photons through an autocorrelation function. Here, we develop an analytical approach for computing short-time nuclear autocorrelation functions in the vicinity of conical intersections, including laser-induced and nonadiabatic coupling between the surfaces. We apply the technique to two molecules of current experimental interest, C6H6 and C6H5F. In both molecules, high-harmonics generated within the same electronic channel are not sensitive to nonadiabatic dynamics, even in the presence of substantial population transfer. Calculated autocorrelation functions exhibit significant deviations from the expected Gaussian decay and may undergo revivals at short (similar to 1.5 fs) times. The associated phase of the nuclear wavepacket provides a possible experimental signature.