My starter is clicking.

1984 Pontiac Grand Prix.
44,991 miles on it.
5.0L 305 V8 engine.

Before I start let me say that the car hasn't been moved since we started working on it. The car was occasionally turned on to check the engine, sounds, leaks, etc. We just did an engine rebuild. The original starter then started to click, so I bought a new re-manufactured starter. After a few days that starter started to click.

I went and had my battery checked and it was bad, I bought a new battery. I put in the new battery, but the starter was still clicking. I then went to have this new re-manufactured starter checked and found that it was bad, strange? I had it exchanged for a new re-manufactured starter. Again it was still clicking.

Finally I got advice that maybe the battery cables were the problem. I went to buy new battery cables. After I put them on I turned the key to turn on the engine but all I could hear is click, click, click. Maybe it is the starter relay, but I don't know where that is, a picture would be helpful.