Ok, I've tried virtually every Corvette Forum that exists but to no avail in getting any help. I hope that since this forum is strictly for C4 owners, someone out there may provide some guidance or has had the same problem and found a solution. 

In order to understand what has happened I need to include this information, as lengthy as it may be so hopefully someone here has an answer:
The problem(s) first began with the ABS warning light coming on in the display information panel. Began troubleshooting the problem using my 1986 Corvette shop manual.

(I have to say that whoever the engineer was that wrote these manuals did not have an editor proof-read them who I'm sure would have recommended a better way in describing the entire manual. They should have used an editor similar to what Chilton has done for years in writing their manuals in every day English)

Traced the problem to the 10 amp gauges fuse in the fuse cluster which indeed had blown. I replaced the fuse and everything was fine for about a day before the fuse blew out again. Before the fuse blew out, the solid State A/C Control Head worked but it started acting funny with several controls not responding and the digital display wondering all over the place. Prior to the fuse blowing out, everything had worked fine.

I even removed and tested all 4 ABS sensors, checked the sprocket gears to see if there were any broken teeth, cleaned out the surfaces on the sensors and re-greased the surface with electronic grease, just as the manual recommends.

Next came the next problem:

The courtesy lights on the doors and under the dash stay on after I close the doors even if I've inserted the key in the ignition switch. Prior to the problems, the lights would turn off when I closed the doors and or started the car. Now the lights will even stay on when I start the engine. After :30 or :45 seconds elapse the lights turn off just as they do when you exit, lock and close the doors. I could live with this, it's no big deal!

Then the next gremlin came calling which is something I cannot live with.
(and please no posts telling me to remove the warning chime, that's not the solution)
Now when I pull the headlights switch to either the park lights or headlights position, the warning chime begins to ring and will not stop ringing until I turn the headlights switch completely off. The chime will continue to ring even if the engine is running. I've already replaced the door jam switch on both doors as well as one door ajar switch on the driver side door with no luck.
All these circuits along with several others are controlled by that proverbial 10amp gauges fuse.  So you're probably wondering: How can you troubleshoot the system if the fuse keeps blowing out. There in lies the rub.
Please help.
George

FYI: My Corvette is a coupe with the 4+3 manual transmission. There are no mods to the car.

Just a shot in the dark as these gremlins are all over the place, but you might check the multi connector on the firewall.....I'd clean the contacts and see if that helps 

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Remember, there's no place like ~ ;)

As far as the courtesy lights on my 86 they stay on for about 30 seconds after I start the car I believe it's normal the headlight chime I had also and it was a bad socket on the front marker light so check all exterior lights good luck

My manual won't be any good for chasing your wiring but by 96, there are still a bunch of dead ends in the manuals that need to be sorted out.

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I have a 93 that had a 40 amp secondary fan fuse that was blown. So you would think that there are only a few connections to check and who knows the fan wiring internally  may have shorted itself to pop a 40 amp fuse or a bare wire to ground as the circuit is hot all the time would fry the fuse. I pulled the fan and it worked so scratch that idea. Pulled all the wiring looking for a bare wire or a break inside the hot or ground wire... All were good. So all that was left was the 2 relays. They both testes as working just like new... i took the fuse panel totally apart , cleaned all connections to make sure all connections were tight and good on that end. Put it all back together and when I reconnected the hot and  ECM wire I found the cause. The hot wire connection to the relay was loose. So it was vibrating causing a bad connection and caused the problem.