Maybe they are...

The ammeter is connected to the horn relay and the starter lug (main harness).  (Black, and black/white wire if I remember.)  It measures a voltage between the two leads and infers a current from the voltage differential.  If you've got higher voltage at the alternator and battery when the car is running, it's charging.  So there's something in common.
 
Remove and clean the terminations to the horn relay, and check that the lugs are securely on the wire ends.

Adam, what do you think? 

We need to clarify the difference between an AMP meter, and VOLT meter. An AMP meter measures Current, while a voltmeter measures voltage...two different things, when discussing meters.
An amp meter runs In Line with the charge...meaning the meter is wired in series with the wiring from the alternator to the battery.
A voltmeter, on the other hand, simply measures voltage, so it is wired with a positive wire on one terminal, and a ground on the other terminal.
A bad Amp meter can certainly drop system voltage after the alternator...if the current going thru it is actually being used up by the gauge, it will lower the available voltage at the battery. An amp meter can also not allow voltage thru it if it goes open, in which case the meter(gauge) would not move at all.
I would certainly clean all of the connections, both at the horn relay, and the alternator. If no improvements are seen, then I would have to suspect a problem with the gauge itself....possibly the resistor/shunt bar on the back of the gauge.
In any case, it appears the charging system IS working, it's just not able to get the full output voltage back to the battery.

Thanks everyone.  And Joel for the difference between the amp and volt meter.  I've ordered a new horn relay but will hold off on the ammeter guage to see if the connections or the horn relay itself were causing my ammeter problem.

There is excessive electrical tape on the wires at the terminals both at the relay and the alternator.  Hate to open all that up but, I'll do what I have to.

I had a similar problem with my 81.  Got new Alternator

|UPDATED|5/17/2013 12:47:00 PM (AZT)|/UPDATED|

Something seams strange if the amp meter goes more negative as you race the engine but measured voltage goes up it seems the amp meter is hooked up backwards. when you go to put back in the new horn relay double ck the wiring hook up. and I think you should inspect what is under the tape you could have corrosion their also. With the car not running and you turn on the headlights does the meter go negative (discharge).

My new horn relay is due on Monday.  In the meantime I'll check out the wiring.  I like to solder everything that's going to be covered by tape.  Oh Me Oh My Oh!  Son of a gun I'm having fun on the Vette-o!!

True.  Except on our cars, the ammeter is not a true ammeter.  It's a DC shunt ammeter.  It carries only a tiny fraction of the total current going through the car's circuit, and approximates current based on differential voltage from two points.  The resistor between the two points causes a voltage drop which deflects the meter one way or another...

Ammeter.  Refer to the below figure.

Troubleshooting the ammeter circuit can be difficult.  The following applies to cars equiped with alternators.  In the Chassis Service Manual there will be a simplified diagram of the charging system similar in part to that show above.   

 

Possibly the biggest mistake that people make associated with the ammeter circuit is not turning the ignition switch to either ACC or ON when trying to decide if the ammeter is showing proper discharge.  You can perform the following test and see if it makes a diference.  Start the engine and let it run for a few minutes until the ammeter reads close to zero.  Shut off the engine and with the ignition switch OFF, turn on the high beam lights.  Make a note of the ammeter reading. Turn off the headlights.  Turn the ignition switch to ACC and again turn on the high beams.  The amount of discharge shown by the ammeter should be about twice, or more, what it was before.

 

By referring to the above diagram, it can be seen that the ammeter reads the difference in voltage between the battery and the alternator.  The wire that goes directly from the battery to the alternator and appears to short out the ammeter is a meter shunt.  What the ammeter actually reads is the voltage drop across this wire.  The resistance of this wire is about 0.1 ohm.  There is no physical resistor in the circuit, the resistance is due to the length of the wire required to get from the starter solenoid to the horn relay around the engine bay.

 

The horn relay is not in the ammeter circuit but is a convenient connection point for the alternator output and the voltage regulator. 

 

When the output voltage of the alternator is greater than battery voltage, the ammeter shows a charge proportional to the difference in voltage.  When the battery comes up to full charge, the ammeter drops to near zero.  If the output of the alternator is less than the battery voltage, as under a heavy load, the ammeter will show a discharge proportional to the difference in voltage. 

 

The voltage regulator is set to have a voltage slightly higher than the fully charged voltage of the battery so that the alternator will carry most of the vehicle loads and maintain a slight trickle charge on the battery at all times the engine is running.  Under normal conditions, the ammeter will show a slight charge when the engine has been running for a few minutes and the system is working correctly.

I'm shocked....
Just kiddin....this has turned into a very detailed discussion, and very informative, I'm sure. Remember, we're working on an early car here.
My point being that there is a loss of charge making it back to the battery somewhere...only a few things can cause that. Bad connections/wiring, or a problem with the gauge itself. The horn relay has nothing to do with the charging system, other than being a common junction box to connect the wiring to. Of course, if the terminals on the relay are corroded, it could create a problem.
The alternator in this case IS working, and the battery is being charged, although perhaps not completely, it seems. The issue is the gauge showing a discharge all the time....even tho there IS a charge getting to the battery.

I'd Like to thank everyone for their feedback. It helps me to solve my electrical problem. I had someone check the alternator before and they said it was fine. Another person said it might be the voltage regulator. Just like the person with the '69, my battery is draining. So I'm going to have to change the alternator.