67 Dart Conv. - No Tail Lights, Park Lights, Flashers

What would cause L8 to only be hot when I push in the brake? The turn signal switch?

I'm not sure quite what is going on but there are a couple scenarios.

Here's what should happen.
Close the switch and electrons flow from high energy 12 Volts through the bulbs and back to the battery ground, 0 volts.
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Now lets say the horn wire H3 is cross wire shorting in the column or column connector.
H3 gets power from the battery.

If there is 12 Volts from the battery shorting to the brake light wire, then stepping on the brake pedal will make it show up in the rest of the line.
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Just because there is 12 Volts that doesn't mean things will work.
With 12 volts on both side of something, electrons don't flow.
Its like taking the garden hose from the front of the house and connecting it to the hose in the back. There's pressure in both hoses but nothing moving.

Now back to the horn.
That relay has one power connection.
Wire H1-16V is always hot.
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Wire H3 is also hot all the time.
When the horn button is pressed, it connects H3 to ground.
Current flowing from wire H1 to H3 powers an electromagnet. That electromagnet closes a switch connecting wire H1 to wire H2 powering the horns.

So H3 may be part of the problems here.
You could disconnect H3 at the relay and see if that returns some things to normal.
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- Matt