You refer to the Pulser Engine Control Unit. Where did you find the reference to 'Engine Control Unit'? In the Service Manual, I could not find any description of a devise or find any reference in the electrical schematics of a pulser associated with the ECU. The only 'pulse thing' that I am aware of is in the electric power steering system. The service manual refers to it as a pulse unit rather than pulser. The steering system pulse unit looks like the part you listed and is located in approximately the same location as you described on the inside back bulk-head. The service manual does not provide a description on the pulse unit function; but, from the EPS schematic it appears to be a signal conditioner for the speed signal that the EPS gets from the differential speed sensor.
Because it is a speed signal, it is reasonable that the frequency of the noise might change as the engine speed changes; however, from the exceedingly limited information in the service manual, it looks like the pulse unit is purely electronic so it is not apparent that it could be making any noise, unlike a mechanical relay. Because it is connected to the differential speed sensor, does it only make noise when the car is moving or does it make noise in neutral at a stop? It should be possible to confirm that it is the noise source by unbolting the pulse unit from its mount and wrapping it in some rags to provide sound damping. Test drive and if the noise is reduced, then perhaps the problem is the pulse unit. Personally, based on the very limited description in the service manual, I am inclined to think it might be something else; but, the noise reduction test should confirm it.