You got a few good replies. You have to diagnose this logically.

First: does the "bat" and other warning lights come on with key in run position before starting engine. If no, then stop right there. Use a standard incandescent test light with one end connected to engine or battery ground. Do not use the alternator case for this test. Disconnect the small push-on wire and connect the probe of the test light with the key in run position. Light "on" means you are getting exciter power to the voltage regulator. In normal operation, this terminal is 0.6-1.0 volts when not charging to complete the dash light circuit to ground. The path is from the push-on terminal, through the regulator, through both brushes (and therefore the rotor winding) to the alternator case, which is supposed to be grounded. This is why alternators with worn out brushes don't charge and also fail to light the warning indicator.

If you did not have voltage at that disconnected wire - the problem is either no power getting to the cluster, bad connections or missing bulbs on it, or open wire from the cluster to the alternator. If this is the case, move the grounded wire of the test light to the push-on terminal on the alternator and connect the other side to the POSITIVE side of the battery. The light should be on. Start the engine and the light should go off. If all this happened, check voltage at the battery for > 13.5 volts. Using the test light this way bypasses everything in the car except the output cable and ground circuit, and allows you to confirm that the alternator can charge, even if the trigger circuit from the dash is defective.

Now... if the dash lights worked correctly in the first place, connect one side of the test light to battery or engine ground and start the engine. Touch the test light to the output stud holding the thick red wire - there should be battery voltage and a bright light. Good so far? Touch the test light to the alternator case (while it's running). Even the faintest glow means a bad ground. Alternately, you can use your voltmeter to check the current carrying paths with engine running. One probe on battery positive other on alternator output stud - voltage should be less than 0.25 volts. Next test; one side of meter on battery negative other on alternator case - voltage should be less than 0.25 volts.

By now, you should have found a definite direction to follow in locating the real failure.