Actually, let's troubleshoot. I'm studying to be an electrician so I'm feeling ambitious.
1. Check your connections, in particular, first you always check your ground and then check where you soldered the fog lights. I'd personally guess a dirty connection is the most likely issue, we're all human and mess things up like this.
2. Connections look good? Now you get to use your trusty voltmeter. Theyre a whopping $8 at walmart, don't splurge too much. Check both headlight connections, each prong, all should read approx 12v. Do the same with the foglights. If all of the connectors are coming out at 12v, then the wiring is healthy, meaning it's a problem with the lights themselves.
3. Individually test the bulbs. Try unplugging the fog lights and then see if your left headlight returns to its normal brightness. If so, it sounds like a current problem. If not, then it's more likely that the LED in the left assembly is giving out. Next, unplug the headlights and try running the fog lights. Will they consistently turn on with the headlights disconnected? Again points towards a current issue. If they won't turn on consistently, then this points back to the loose wire theory.