GEN Light glows dim on my '68

I recently got my hands on a '68 convertible that's in pretty good shape. One issue it has that I've been trying to figure out is that although the charging system is working fine, the GEN light on the dash glows at about 1/4 brightness when the car is running. It also glows only dimly when the car is not running but the ignition switch turned to "on", when the light should be on at full intensity. I tried cleaning the connector to the regulator and the next time I started the car, the light went off for a second, but then came on again and continues to act this way.

Any ideas? Thanks.

Take a look at the car at http://www.americantorque.com/page/1/1048/http://rides.webshots.com/album/564065271YcoOOE