With the headlights on, the left signal light does not work and it causes the engine to downshift whenever I use a turn signal. When I turn on the highbeams, the left signal light stays on, but only the right highbeam lights up.

Based on the symptoms you described, it seems like there may be a short circuit in the wiring or a problem with the headlight harness. When you unplug the headlight harness and the issue stops, it suggests that there may be a problem with the wiring or a component in that harness.
One possible cause could be a faulty turn signal switch. The turn signal switch controls the operation of the turn signals and can cause strange behavior if it is malfunctioning. It may be worth checking the switch to see if it is causing the issue.
Another possible cause could be a short circuit in the wiring. A short circuit can cause electrical current to flow in unexpected ways, leading to unexpected behavior like what you're experiencing. It may be worth inspecting the wiring for any signs of damage, such as frayed or exposed wires.
If neither of these solutions help, it may be worth consulting with a mechanic or electrician who has experience troubleshooting electrical issues in vehicles. They may be able to diagnose the issue more accurately and suggest a solution.

it's the grounds if they're both flashing fast it's definitely grounds take a test light and see if its got power goes through the test light grounded to the frame and if the light comes on then it's definitely your grounds

The headlight and turn signal are on two different switches and two different circuits. The main thing they both share is a ground connection.
I would check the ground and sockets for both the headlight and turn signal next.

Check front and rear lights to see if the wiring is arcing to the turn signal on the left side of the car. This is the best guess as it's simply a wiring problem and nothing else, as there is too much current being forced through the turn signal when the headlights are on. Headlights draw much higher current than the intermittant turn signals and therefore pops the fuse.

All types of car headlight problem troubleshooting.Click the link below :---All headlights not working? http://repairhelpcenter.blogspot.com/2012/01/all-headlights-not-working.html
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Changing front, right turn signal on 2005 Buick Terraza: Open hood; when facing the front of vehicle, the right turn signal is on the passenger side (left). The headlight assembly needs to be removed to easily reach the turn signal. On my vehicle, there is a 10 mm screw on the left side. Remove it. There is L-shaped pin on the right side of the headlight assembly. Swing the pin counter-clockwise (to the left). Pull the pin straight up to remove. The headlight assembly is now loose, but there is a pin snapped in a socket on the back of the assembly that still holds the assembly. Pull the headlight assembly hard and straight to the front of the vehicle. When it snaps loose, the assembly is now held just by the rubber gasket surrounding the assembly. You need to gently work the right side of the gasket out of the grill cowling. The assembly should pull straight out. The wires are long enough to lay the headlight assembly in the engine compartment. Finally, the turn signal is now accessible. Twist the light holder counter-clockwise and pull out the light holder. Change the bulb. Do not punch your man-card for credit until you have successfully reinstalled the headlight assembly. It goes back in a little easier the second time. Once you have put the L-pin in place, the screw back, and successfully tested the lights, you can now punch your man-card.

I give the mechanical engineers and designers a D-minus instead of an F only because I was successful on the first try. No light bulb on anything commonly used by people should be this hard to figure out.

nope you got a bad ground either at the light sockets or body ground

I'm no expert, I recently purchased a 2003 vibe. I noticed the automatic headlight's sensors can be super-sensitive, about an hour hours before dusk they'll kick my headlights on (when the sun is still shining!), or sometimes when I go into an underpass, and then sometimes they'll realize it's light enough and turn themselves off. This would cause your dash lights to go to the 'headlights on' mode and turn the headlamp signal on, the intensity is controlled by the dimmer/dome light control on the left side of the dash. Check to see if the dimmer is down too far, as this could cause the lights to dim when the automatic headlights turn on. It's also possible that the dimmer is not working, thus no power is getting to the dash lights through the dimmer. Try testing it by starting the car in daylight, then manually turn on the headlights, then adjust the dimmer. Like I say, I'm no expert, just guessing because I've noticed it happen similarly on my Vibe, but my dimmer was at half-way, as I like it for night driving. Someday, I'd like to disable the automatic sensors and DRL.

Sounds like the jolt from the barrier has caused a bad ground to occur. Look for a bad ground wire around the left headlamp in or around the headlight bucket.
Tighten or replace the bad ground wire. A poor contact will cause the headlight to light dimly.

check your fuses, something is blowing out your bulbs or causing a lack of electrical support, and cant support all your lights working at once...let me know how it goes