---If it says 12v, then I would guess it is your battery. If it's a small box with removable top, then yes, that would be either engine management or relay cluster. Check the repair manual for a starter relay location. Either way, there should be relays inside that box and there should also be a spare relay for testing/replacement. Remove the relay that is clicking and either replace it with the spare or another relay for say, coolant fan if they're the same. You won't need the cooling fan to quickly test for cranking. Also check all fuses that are in that location.
---Loose or dirty connections on the battery will cause a rapid clicking sound, which is the spark arcing around between the terminal and the post. Never allow your "mechanic" or anyone else to twist your battery terminals to see if they're tight. This can and will cause damage to the post where it is connected to the plates inside your battery. Either they're tight or they're not and a wrench will give the answer. Remove them, clean both the battery and the terminal, replace and tighten them.
---If your vehicle has the cheap tin clamp-like battery terminals that look similar to a hose clamp. My suggestion is always to replace them with quality terminals or cheap terminals of a good design. Eliminating lead is always a good thing but replacing cheap, tin terminals with a set of brass, marine terminals is as easy as can be. Living in AL, I had to work on a lot of Katrina refugees' vehicles and oftentimes when they thought they had a major problem, it was related to the cheap terminals found on most Fords and Hondas. I never can find an image of these terminals, so again I'll describe them as, "look like hose clamps". Even the slightest crack in the least obvious place is enough for these terminals to lose contact with the battery post. As most know, when something is cool and you tighten it down, when it heats up it will expand and become stressed. Stress causes... yeah.
---This is what you'd want to replace them with if you have the cheap tin hose clamp-type.
---Using as much of the original battery cable as possible, cut just the ring off the terminal and enlarge the bolt hole to fit the marine terminal. Section A of the below image is the original terminal (cheap, tin, clamp-type) and section B is what was saved and mounted on the marine terminal. Mount all wires to the correct terminals in the same fashion if need be.
---FWIW, this also gives you a solid mounting point for your fused amp/capacitor circuit or other accessories.