My research turned up that on 1983 eldorado's equiped with the guide-o-matic auto dimming option used a dimmer relay located near the fuse block.
The elect schematic's I located (see attachment) shows this relay just ahead of the headlights. The relay is approx 1" by 2" pluged into a 5 wire harness terminal. The relay consist of two functions, one is a small solinoid activated by the colum lever or photo-eye. The second is the switch controling the power to the headlights. (note: the highbeam is the normal contact). The solonoid windings get hot and tend to fail activating the switch to low beams.
The fact that this relay gets hot and locks the highbeam setting when it fails speaks for its shelf, ie; melted plastic / wires ect. / fire!! if not replaced and use of the headlights is continued.
I located thru my local GM Parts supplier a replacement at GM Vintage Parts. The orig part number on the relay matches the current order number (Guide#5969007 12v) and cost me about $60.00.