If these truly are the wires for the dome light, then they simply get
connected together. I have a service manual (found on the web) for the
'96 - '00 Civic, and in that manual the wires for the dome light are
described as LT GRN/RED and LT GRN/BLK (Not RED and RED/BLK as you have
found). According to that manual, the RED/BLK wire is live whenever the
parking lights are on (including when the head lights are on). The RED
wire is from the dash lights brightness controller. All the dimmable
lights in the dash are wired between this RED and RED/BLK wire, LOWER
voltage on the RED wire means BRIGHTER dash lights. Your after-market
stereo probably has a display illumination wire. Try connecting it to
the RED wire and see if the display illumination can be adjusted with
the dash lights brightness controller. If you are lucky, it will work
just fine, in which case you carefully tape off the RED/BLK wire to
avoid shorts in there. What you might see is that the stereo display
gets dimmer as the dash lights get brighter, or you could see a host of
other anomalies. If so, tape off the RED wire carefully and connect the
RED/BLK wire to the stereo display illumination wire.
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