A new wave of electric vehicles for personal mobility is currently crowding public spaces. They offer a sustainable and efficient way of getting around in urban environments, however, these devices bring additional safety issues, including serious accidents for riders. Thereby, taking advantage of a connected personal mobility vehicle, we present a novel on-device Machine Learning (ML)-based fall detection system that analyzes data captured from a range of sensors integrated on an on-board unit (OBU) prototype. Given the typical processing limitations of these elements, we exploit the potential of the TinyML paradigm, which enables embedding powerful ML algorithms in constrained units. We have generated and publicly released a large dataset, including real riding measurements and realistically simulated falling events, which has been employed to produce different TinyML models. The attained results show the good operation of the system to detect falls efficiently using embedded OBUs. The considered algorithms have been successfully tested on mass-market low-power units, implying reduced energy consumption, flash footprints and running times, enabling new possibilities for this kind of vehicles.