OK, was thinking you were referring to the Circuit Opening relay. With a relay, any relay, there are two components involved in making it work properly. One is the coil(s) that energize and create a magnetic field to pull in the contacts. That is the click you hear. The second part is whether those contacts really make electrical contact sufficient to conduct the current the load needs. If those contacts are pitted or dirty, you may not get enough current flowing to power the load, in this case the fuel pump.

The fact that the CO relay is clicking says that it is getting power from the main relay, as that is what supplies power for the CO relay coil and it's contacts as well. So you could either check the voltage someplace between the main relay and the CO relay or check at the fuel pump.