Variable clacking sound is making me crazy
 

I have a '79 SC. My rebuilt engine has about 5K miles on it. I've had a recurring noise before and after the rebuild that I cannot figure out - it seems to come and go...

It is a loud clacking noise. There is no noise at idle, regardless of engine speed. The noise seems to only occur at lower speeds, and only under acceleration or deceleration. If I accelerate (and have the noise) then back off the gas and maintain the speed, the noise stops. If I take my foot off the gas, the noise comes back until it slows. It sounds like metal hitting but seems linked to air flow (accelerate or decelerate) or torque. It doesn't happen at cruising speed. The worst thing - it doesn't always happen. I don't think it's related to air temp. My wife thinks it happens after a hard left turn, but then eventually goes away.

Any ideas where to start ? I do hear a faint noise in my air pump at idle/ I thought of removing the belt to see if this could be it but not sure if this would be a bad thing to do.

You still have the secondary airpump connected? Try disconnecting as see whether the noise disappears. I'd keep it off anyway.

CV joints do that.

I had a similar problem after first buying my car. It turned out it was my rear shocks. They were making a rattling sound and I thought it was in the engine.
May be worth a look.