You definitely got some electrical issues going on. The entire engine (and front end lighting) harness unplugs from the bulk head. If you cannot determine the issue/s, I would recommend removing the engine harness and either replacing it or go through it. You need the wiring diagrams and to be honest, you need all of them as despite what you would think, many times you need to look at several to figure what is doing what. It isnt hard, its tedious and detailed but it certainly can be done. Personally, I would remove the existing engine harness and replace it if it has been altered. Now, if you are running things like a MSD ignition or something, you need to make concessions for that.
The other option is removing or at least uncovering the existing harness and ensuring everything is going where it is supposed to.
From what you have posted, you have power back feeding into your system somehow.