I suppose what you are hearing is the solenoid.

You turn the key, the pulse module commands the solenoid to engage, when it engages the heavy current the starter draws causes the available voltage to drop (due to the problem we are chasing) and as the voltage drops, the solenoid drops out. When the solenoid drops out, the voltage goes up due to no starter load, so the solenoid then engages again and the process repeats.

The voltage is dropping because of high resistance in a battery cable or connector, or because of a bad battery. The battery ground wire goes to the chassis wall just ahead of the battery, open the hood and LOOK AT IT. Is it in horrible shape? I replaced my battery ground cable within a month of buying my car (along with the battery) just to avoid stuff like this.

Have you looked over the battery ground connection at the battery? Look at the lug at the chassis connection. This is right ahead of the battery.



WAIT A MINUTE - there has to be a large, high current ground cable from the engine block to the chassis. Any chance you left this disconnected / damaged it during the clutch replacement?