A vehicle rear lamp, comprising: - a casing; - a plurality of light sources disposed in the casing, among which at least one light source (23, 24b) the activation of which depends on the lateral positioning of the lamp on the vehicle; - a connector mounted on the casing to enable the connection to a bundle of cables of the vehicle, the connector having: - a first power supply terminal and a second power supply terminal intended to be connected, the one to a positive power supply cable of the bundle and the other to a ground cable of the bundle; - at least one communication terminal (53, 54) intended to be connected to a cable of a multiplexed communication medium of the bundle, such as a CAN bus or a Lin bus; - a power supply circuit housed in the casing linking each of the light sources to the first and second power supply terminals (51, 52); - a control unit housed in the casing, which is linked to the or each communication terminal (53, 54), and which is arranged to be able to control the activation of one or more light source(s); characterized in that the power supply circuit includes a module which has a first input node linked to the first power supply terminal, a second input node linked to the second power supply terminal, and an output node linked to the light sources, the module including: - a rectifier device configured to deliver to the output node a power supply voltage equal to the absolute value of the voltage between the first and second power supply terminals (51, 52) in operation; - a polarity detection device connected to the control unit and configured to provide the latter with a data indicating which of the first and second power supply terminals (51, 52) is connected to a positive power supply cable in operation. - a casing; - a plurality of light sources disposed in the casing, among which at least one light source (23, 24b) the activation of which depends on the lateral positioning of the lamp on the vehicle; - a connector mounted on the casing to enable the connection to a bundle of cables of the vehicle, the connector having: - a first power supply terminal and a second power supply terminal intended to be connected, the one to a positive power supply cable of the bundle and the other to a ground cable of the bundle; - at least one communication terminal (53, 54) intended to be connected to a cable of a multiplexed communication medium of the bundle, such as a CAN bus or a Lin bus; - a first power supply terminal and a second power supply terminal intended to be connected, the one to a positive power supply cable of the bundle and the other to a ground cable of the bundle; - at least one communication terminal (53, 54) intended to be connected to a cable of a multiplexed communication medium of the bundle, such as a CAN bus or a Lin bus; - a power supply circuit housed in the casing linking each of the light sources to the first and second power supply terminals (51, 52); - a control unit housed in the casing, which is linked to the or each communication terminal (53, 54), and which is arranged to be able to control the activation of one or more light source(s); - a rectifier device configured to deliver to the output node a power supply voltage equal to the absolute value of the voltage between the first and second power supply terminals (51, 52) in operation; - a polarity detection device connected to the control unit and configured to provide the latter with a data indicating which of the first and second power supply terminals (51, 52) is connected to a positive power supply cable in operation.