Everything seems to work great except that when I use headphones to listen to the player through my stereo I can hear a high pitched whine.
Classic ground loop and/or inductive noise problem. Use the same techniques to eliminate this as you would if it were installed in a car:
http://www.installdr.com/TechDocs/999501.pdf
http://www.installdr.com/TechDocs/999502.pdf
http://www.audiocontrol.com/techpapers/tech1002.pdf
Originally I had the permanent power wire supplied with 12v but the empeg would turn off periodically with that wire connected.
This indicates something wrong with the power supply, or incorrect wiring. Do all your problems go away if you disconnect the AT power supply and feed it from the AC adaptor that came with the Empeg?
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Tony Fabris