Since you have a multimeter try a volt-drop test to determine whether or not you have a bad connection somewhere. Checking continuity is fine but it does not check circuits under load, and since a starter motor will draw well over 100 amps a load test is what you need to do. Using a voltmeter is the best way to do this.

Remember a voltmeter measures difference between two points of a circuit. It does not measure current, or give an indication of whether or not current is flowing.

Connect you red probe to battery positive, and the black probe to the starter terminal. Since they are both positive (you are measuring two ends of the same cable) the difference should be close to zero. It will never actually be zero because there will always be some loss, even if only a few millivolts. Turn the key to the start position and observe your meter reading. Whatever the meter reads is the voltage difference between the red and black probes. It must not show greater than 0.5 volts when under load. If it does then you have a poor connection on this cable or terminals. Do the same test between the engine block and battery negative to check the engine earth. Again you should see not more than 0.5V difference when you turn the key. If you do clean the connections and repeat the test.

Connect your probes to both large terminals on the solenoid. Initially your meter should show 12V, but when you turn the key it should change to close to zero. Any reading will indicate a poor connection across the solenoid terminals, which again should not exceed 0.5V.

The clunk in your case could also be the starter pinion getting stuck in the flywheel ringear.....