When I add a circuit to the electrical bus, everything browns out (dips). For example, when I turn on the lights then hit the brake pedal all the lights dip out. I have replaced the regulator, distributor and tested the system with a brand new battery. The problem still is present.

There is more than one thing that can cause these symptoms. But the most common thing is a bad connection at the battery terminals.

Remove the posts, scrape the battery tops and the inside of the cable clean, lightly coat the bare metal with oil or grease, then put them back on. See if that fixes it.

all scraped out, posts and cable connectors, I even removed some lead from the clamp of the connector to ensure a stong connection. alas the problem still exists. The radio even shows the problem by clicking, although it is not constant it is a reminder of the problem. And no its not a big deck with amps, its the stock am deck.

also, the car has a flat spot at about 10% throttle, and it sometimes stalls out while the lights dim 50% at the same time...

Check just where the main wiring looms comes into the cabin, there is a large white wire, when resistance builds up at the connector, temperature rises and fuses the connector together, it is also in the same connector as the brown wire which is your idle shutoff soleniod. Worth a look?
The white wire feeds all power to the cabin!

I pulled that and every other connector apart from the wire loom and inspected them for any pitting or unusual coloring but everything looks normal. I have also pulled out fuses one by one to see if I can isolate the bad circuit if there is a short present, but still the problem is there.

you may need to get a multimeter and check for voltage drops.

Hey Keith, are you the guy in Vancouver?

Anyways, I would definitely check the connections on your battery and the main power to fuse box plus ground wires. Did you check what voltage the system runs at?
The alternator should put out enough that the battery will charge up. Have you added anything lately? New driving lites or something? Maybe you created a problem.

Does the engine lug down too?

Try to give us more info to help ya out with.

Yeah, Im in Vancouver. I havent checked the system voltage and Im sure how to check it. The battery doesnt seem to be the problem because it is a full 13.7 volts and over 15 running. Starts are fine. No additional electrical devices have (ever) been added to the electrical bus, its all stock, a.m. deck...
The engine does seem to die with the electrical, sometimes, usually in the mornings or when its ben cold for a while. I do let the car warm up to half on the temp guage before this happens though.
Reving the engine brightens the lights by maybe 5%. You can hear the heater fan speed up as you increase throttle as well, as leaves spit out the defrost ports 8)

Hope this helps you, help me.

Oh, and I checked the ground, I thought it was strange that the grounding bolt was threaded into a hole that the threads were coated in paint. so Im not sure that the ground is totally earthed out, if you know what I mean. Is there a way I can check that?