It could honestly be either, how many miles are on the thing? Did it start to do this gradually or all at once? After it rained?
When a fuel pump goes, it can also take out the relay as it's the source of power for it (increased resistance=increased heat=toasted relay). A relay is also easy to swap in and out to see if it's the culprit, any CB-1 buddies nearby you that can do a two second swap?
Don't also rule out wiring and the like. If it has a crummy ground, bad connectors or corroded wires, it could cause it to do the same thing as well (the clicking and the noise).
Check your wiring first, then the relay and then the pump. At least that's the way I would go. I'm not too knowlegeable about Honda CB-1s but that's what I would go through on a vehicle with a fuel pump. If you have a manual and it gives a flow rate, you can test the pump and rule things out that way as well. By the sounds of it, with the clicking at the pump, I would assume that first.
-Randy