The lamp comprises at least one light-emitting diode and an electronic power switch connected in series between a power source and the light-emitting diode. The electronic power switch is controlled by an electronic processing circuit according to the state of a control button connected to a control input of the electronic processing circuit. The button is connected in parallel to the electronic power switch. To detect and reconstitute the state of the button, the electronic processing circuit periodically applies fine turn-off pulses to a control electrode of the electronic power switch.