your relay is fed off the reverse lights? the Cold monitoring happens periodically when the light is off, the hot monitoring is happening periodically when the light is on... it is not a continuous signal, there are series of short bursts hitting the bulb, in most cases not long enough to overcome the induction of the relay and to activate the relay... waht you are probably experiencing is a PMW - Pulse Modulating Wave, a signal coming from the LCM that modulates the intensity of the light output by modulating the 12 VDC - a constant series of 0V with 12V (nominal, actual values are 0.5 VDC to 14VDC) with gaps of 0 Volts DC and 12 VDC spaced so the light output is either dimmer or brighter, depending which level of voltage is held longer...

10 Hz pulsating is rather high, which makes me think, that there might be another issue at stake - the lights are powered by the LCM, which powers the lights via transistors, and may so be, that the additional load of an automotive relay that is being used is too much for the sustained current on the transistor's collector, and it is cutting in and out, thus creating the "pulsating" effect... if that is the case, you may eventually fry the transitor inside the LCM, which will render the module defective... applying a direct +12 VDC to the light bulb while it is connected to the LCM may burn the back end of the transistor that powers the light bulb, again, rendering the LCM defective - you should be careful, as the LCM also stores the mileage information of your car...

you may wish to consider replacing the automotive relay with the one with a smaller current draw (see this post http://www.xoutpost.com/918829-post36.html for the spec on the relay that I would recommend)