Low- and intermediate-mass stars eject much of their mass during the late, red giant branch (RGB) phase of evolution. The physics of their strong stellar winds is still poorly understood. In the standard model, stellar pulsations extend the atmosphere, allowing a wind to be driven through radiation pressure on condensing dust particles. Here we investigate the onset of the wind, using nearby RGB stars drawn from the Hipparcos catalogue. We find a sharp onset of dust production when the star first reaches a pulsation period of 60 days. This approximately co-incides with the point where the star transitions to the first overtone pulsation mode. Models of the spectral energy distributions show stellar mass-loss rate suddenly increases at this point, by a factor of ~10 over the existing (chromospherically driven) wind. The dust emission is strongly correlated with both pulsation period and amplitude, indicating stellar pulsation is the main trigger for the strong mass loss, and determines the mass-loss rate. Dust emission does not strongly correlate with stellar luminosity, indicating radiation pressure on dust has little effect on the mass-loss rate. RGB stars do not normally appear to produce dust, whereas dust production by asymptotic giant branch stars appears commonplace, and is probably ubiquitous above the RGB-tip luminosity. We conclude that the strong wind begins with a step change in mass-loss rate, and is triggered by stellar pulsations. A second rapid mass-loss-rate enhancement is suggested when the star transitions to the fundamental pulsation mode, at a period of ~300 days.