The "click" isn't everything though.
In fact as far as failure modes go, the click is nothing.
Lack of a click usually indicates a failure upstream of the relay itself, the switch or wiring that tells the relay to turn on and off.
Most relay failures involve the high current contacts on the output side. Corrosion and or crud builds up, and sooner or later, the relay just fails to pass current, even tho it is switching and mechanically it is working fine.
A good example of this is the "boost relay" in my Monaco. This is a BIG relay, kinda like a Ford starter solenoid, but made for continuous duty.
In my coach, it is energized by both the boost switch (intended to connect both battery banks in an emergency)and the "BIRD" circuit (intended to connect both battery banks for charging.)
My BIRD circuit always worked. Both banks charged no problem.
But if I ever let the chassis batteries get low in storage, hitting the boost button did nothing.
I could start the genny (it's on the house batteries) but the diesel wouldn't crank when I held the boost switch down, even though I could hear the relay click.
The problem turned out to be severe gunk and corrosion inside the relay. The contacts would pass the relatively small battery charge current no problem, but too much resistance to pass enough current to crank the cummins.
I Was able to take it apart and clean it, and now I can disconnect the chassis batteries, hold the boost switch, and the cummins will crank right over and start.