The clicking may well be the starter solenoid actuating to switch power to the starter motor.
The starter motor might be bad
A power connection to the starter motor might be bad
The battery might be low on power
When the battery becomes flat on my little Escort the clicking symptom is what happens.
The voltage might appear to be OK but if the starter tries to draw the high current it needs the voltage will drop to be very low indeed - the starter solenoid drops out because of the low voltage - the starter stops drawing current - the voltages goes back to a higher value and it all happens again - click-click-click.
I suspect a battery on the way out. How old is it?
I am not a motor engineer - this is just a guess.
Good Luck..., December 2015