I have a 1987 BMW 325e 4 door, 6 cylinder with an Automatic transmission. A few weeks ago it started blowing a single 7.5 amp fuse. The fuse is the one that controls the license plate lights, rear lights on the driver’s side and parking lights in the front on the passenger side. At least that is how the fuse is labeled. It also shuts down the dashboard instrument lights. Other lights on the fuse that it says controls the dash lights continue to work fine. Headlights and such are not affected. I noticed that if the dash lights were turned down all the way, the fuse would not blow and, although I couldn’t see the instruments at night, all the exterior lights worked properly. I figured it must be the headlight switch rheostat that controls the dash lights, right? So I replaced the switch, with no effect. When I turn the dash lights up, the fuse blows and I lose the lights associated with that fuse. I have searched the wiring and have not found any breaks or burns. Anyone else have a similar problem or a possible answer? I am open to suggestions! Thanks… 
You have a short somewhere direct to ground. You have isolated it to the dash light circuit. You need a circuit tester to find the short. This will involve considerable underdashaerobics. Good luck with your search for this little monster, these can be hard to find. I would venture to guess that you did not find a burn because the fuse is doing its job.