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is the solenoid apart of the starter?
Ok this might be a bit in depth so please bare with me.
What you have is a starter solenoid. What that mean is the solenoid is apart of the starter. Normally the click you are hearing is the solenoid trying to connect.. If you look at the solenoid like a switch what you hear is the switch trying to connect.
So here is where knowing some info will be able to help me pinpoint it for you.. if you look at your pic the blue wire that is going to just to solenoid, that wire should have 12 volts and its job is to active the solenoid.. If the solenoid is bad it will just click but you will have 12 volts to that wire... however if the voltage is low to the solenoid it will also just click.. this is why i asked if you had a volt meter.
Here is a few things you could do.. you could replace the solenoid however the cost of the solenoid is near the price of a starter.. So replacing the starter would be the best thing in this case.. however it could be explensive. also if you replace the starter and the problem still is there.. from there we would have to figure out where in the wire harness you are lossing voltage. I hope this helps.
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