Early A Horn Blows on Left Turns

Update: Up until now, I have been working on problems with the front turn signals. Recently, they began functioning. But another problem showsed up at the rear. Will it never end?

Forgot to mention that when I recently replaced the flasher with one I purchased at AutoZone, the green arrow dash lamp flashed about twice as fast as normal. That was fine with me because I prefer faster "flash". However, when I checked around the outside of the vehicle, I found the left rear turn signal was not flashing (although the green dash light, which normally shuts down when there is a bulb problem, kept working). Then I found the left rear brake light was not working either.

I checked the mini-lamp and it was OK. I replaced the mini-lamp anyhow and still nothing. Keep in mind the left rear parking light is working all this time. I checked voltage at the bulb socket wire inside the cavity and found 0 volts. Checked it again later and found 10 volts. Checked it a later a third time and found a little more than 12 volts. Checked it again and found back to 10 volts. All this time, re-inserting the bulb in the socket each time, I found the filament for the brake/turn signal would not work, only the parking lamp filament. I even ran two extra ground wires from the lamp socket, but still nothing. Tried things with the engine off and the engine running. Checked battery voltage: engine off 12.7 volts and running 15.11 volts.

Now I don't know if the new flasher was faster because that would be normal for that particular flasher (has an imprint on the base "max 4 bulbs) or if it flashes faster when it perceives a lamp malfunction in the system (unlike the factory system which seems to shut down the dash monitor lamp).

I'll keep trying.