96 corolla relay clicking

How long was the car shut off before you opened the hood? Do you have power windows? Are you sure it was a relay that was clicking and not the normal ticking sounds that come from an engine that is cooling off?

There should not be any relays clicking when the engine is shut off.

Which relay was clicking?

Does the car have any aftermarket accessories like a security system, remote lock/unlock, or remote start, fog lights, etc?

A relay generally will not make clicking noises on its own unless power is supplied to it. It is possible that the switch that is supplying power to the relay, or a short circuit is causing the condition, not the relay itself.

Yeah, which circuit was it? All the relays are clearly marked on the cover of the fuse box, unless this was some aftermarket thing like an alarm of driving lights, or what I do...put a relay on the Power Amps so I KNOW they're off when the car is off!