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So long story short I have a 79 corvette, was an automatic and I just swapped a TKO 600 5 Speed in this past weekend/ few days. While I was doing that I ordered a new Retrosound Radio to replace the (poor decision from my younger self) pioneer radio I had in it before.
After finishing the project and starting it up I had a few things messed up, my Tac didn't work and I swapped my neural safety switch and reverse lights cables. So I fixed both of those things, but the last thing I couldn't fix. When I have my lights on, my interior backlights to all my gages, center console and speedo/tac gage all do not come on unless I have the high beams on... I haven't been able to figure it out.
The only thing that struck me this past day was all of the connects on the radio basically swapped out one for one, minus the Illumination/Dimmer connect to my old radio I did not have a connection for that, but didn't think it would affect the entire cockpits lighting.
It sounds like it might be missing a ground? The illumination wire could have been providing ground thru the lights in the old radio, and the high beams might be proving the ground connection also. To verify this, you could connect a bulb to the illumination wire, and connect the other side of the bulb to a good ground. If that fixes your dash lights, then you need to find the ground that is missing.