Hi,
I agree with some of the previous posts - get the following as a minimum:
Test Light:
Quick way to check power and grounds etc.
Multimeter:
Measures DC Volts, Reistance (Ohms), Current (most limited to 10 or 15 Amps DC). Must have for electrical diagnosis.
GOOD wiring diagram:
The AIM has a wiring diagram but I find it leaves a lot to be desired. Several of the vendors sell wiring diagrams but these are basically the same wiring diagram as in the AIM with a few other diagrams thrown in.
TC member 69-er sells a color wiring diagram on Ebay for 1969 Camaro. The wiring is almost identical to 1968 and is done extremely well (one significant difference is the ignition switch connector - switch was dash mount in 68, steering column mount in 69). I also have a 1968 RS and rely on this as my "Go To" wiring diagram. He breaks down the diagrams into functional sections (e.g. Charging, Starting, Power Distribution etc.). He also includes chapters on troubleshooting which may be helpful to you. I believe it comes as a pdf file. Here is the link (I think he has 1 left):
1969 69 Camaro Electrical Troubleshooting Manual with FULL COLOR WIRING DIAGRAMS | eBay
I agree that you should acess the wiring you have. Is it stock? Upgraded for aftermarket electronics etc. What is the condition? Are there a lot of hacked crimp connectors in the wiring? Wire Nuts (arrgh - really bad sign). If it is intact I would diagnose the problem(s) before ripping it out. If it looks like a total hack job then you might consider something more drastic.
But start with the basics. Note what works and does not. Go back to the wiring diagram and see if the things that do not work have a common electrical path (turn signal switch, fuse, GROUND) and check those points first. Check whether power is present along the wiring. I usually start with the easy to access points in the wiring like the light socket, fuse and work my way from there breaking down the path.
DO NOT underestimate grounding. Weird electrical problems can many times be traced to bad grounds. If a ground is bad, current can sometimes find its way around and through paths you may not even think of.
If you want list the things that work and the things that dont. Might help folks here provide input.
Hope this helps -