Well right there's your problem.....red wire's bad!........lol
Looks like a relay, but if you have turn signals, it might be a flasher can.
If you intend to keep this vehicle, I truly believe your beast course of action would be, as you already know, rip it out and start over. It all may work now but later on, it will be a maze of "which wire goes where". There are tons of re-wire kits avail and there are just as many opinions as to which one is better........... I tend to use the Painless kits, not the cheapest, but I am very satisfied with the quality and ease of installation. Just about every kit has labeled wires and fuse boxes etc........
My 1st re-wire took a couple to three weekends to install. Easy day really, don't do what I did and leave the old one in and remove it as I went, didn't work out well for me, ended up removing the whole thing. My suggestion is start removing the old one taking pictures of all connections and use masking tape to label where it physically came from. When you start to put the new one in, solidly mount the fuse box 1st and run the wires to where they will generally end up, then starting at the fuse box place the wires in the finial resting place, using wire ties for each side of a turn, corner, obstacle, tying and securing everything tightly in place. Then and only then make your final "proper length" cut.
I didn't and ended up with a mess, ended up undoing just about every connection and re-doing the length. Don't leave extra length in the harness wires for "later on" trouble shooting, again I did and it was a mess. If you want a wiring diagram, draw one before you put the thing in the car, again I didn't and in the end , I removed the entire harness from the car, made my diagram and when I re-installed it in the car, I did it correctly and everything went smooth, except for all the re-terminations and those pesky 4 inch wire section I had to cut off.....lol