Could be a number of things.
You seemed to have eliminated the battery, but for the record, a battery that has sat around with little use undercharged can sulfate and cause this.
It could of course be the regulator
Take a GOOD hard look at the ammeter, with the car off and all loads shut down, and make sure it's not off center
Next is voltage drop in the grounding and wiring harnesses. Nowadays, the firewall / bulkhead connector is a suspect.
Get a digital meter, preferably one with a bar graph underneath the digits, so you can see "analogue" changes, and measure some voltage drops.
Put one proble RIGHT ON the battery negative POST, and the other probe RIGHT ON the regulator mounting base. There should be VERY little reading, the less the better. Anything approaching 1/2 volt or more means you have a grounding problem
Same thing --put one probe RIGHT ON the battery positive post, the other probe on the ign terminal of the regulator. Here again, the lower the reading the better. Anything approaching 1/2 volt means you have a drop in the harness, which goes from the regulator/ igniton--through the firewall connector--to the ign switch connector--through the switch--back out the ign switch connector--through the ammeter--back through the firewall connector--and back to the battery. ANY of these connections can cause a drop, which will cause the regulator to "try" and compensate.
Measure right across the battery terminals with your digital meter. With all loads off, the battery at full charge, warmed up, and the engine at a good fast idle or better yet, "low cruise" the meter should read above 13.5, up to 14.5, and below 15.