Phone calls nobody there?

It could be a telemarketer. Lots of them have automated systems that dial number after number. If nobody answers after a certain number of rings it goes onto the next number. If someone does answer, then it clicks and alerts the telemarketer that someone answered the phone. Lots of times the telemarketer isn't prepared for this to happen, so they take awhile to click in and start talking to you. That might be what is happening to you, I'd almost bet on it. I wouldn't bother with the caller ID option for that reason. Just hang up if you hear a click.