This study describes a simple method to generate sub-20 fs UV-pulses (264 nm) by third-harmonic generation, in an air-plasma filament formed after focusing the fundamental 800 nm beam directly in the lab open-atmosphere. The generated pulses are applied to track the relaxation through the conical intersection that couples the S2 and S1 states, in the benchmark molecule of naphthalene. The transients, with a resolution of about 25 fs, show two differentiate patterns of quantum beats. The assignation of these oscillations to specific modes in the lower S1 state and to electronic coherence between the two coupled states is discussed.