We report an experimental technique to trigger modelocking (ML) emission in frequency-shifted feedback (FSF) lasers. These lasers feature an intracavity modulator driven by a radio frequency tone, which shifts the light spectrum every cavity round trip. The technique consists of the drive of the modulator with a second tone at the cavity free spectral range (FSR) frequency. So, in addition to the frequency shift, a weak amplitude modulation (AM) appears synchronous with the cavity round trip time. The approach is successful as FSF cavities support chirped modes evenly spaced by the FSR, whose AM coupling produces convenient seed pulses for the ML onset. This results in ML emission at arbitrary frequency shifts and initiation thresholds lower than in standard, spontaneous FSF laser ML. Simulations indicate that the role of AM is to trigger the formation of ML pulses, but the primary mechanism of pulse buildup is the Kerr effect. The technique opens a new, to the best of our knowledge, practical route to initiate ML emission in FSF lasers.