I don't get this part: “I jumped the tail light to the parking/clearance light to achieve almost twice the brightness." Pardon my abrupt jump into this but this reminds me of having a manifold air leak and happily adding more gas to fix it.
My 1st guess is I think you found a bad connection, too much resistance for the current that light needs, but that doesn't go down the right path: the LED draws less current than the filament bulb by 0.04 W vs 6 to 10 Watts. That's 150 times less current. That tells me you would have noticed the issue with the old bulbs being very dim. Maybe this wasn't there before and maybe something is wrong in the wiring now and you fixed it by bridging the problem. Point is something is wrong in the wiring and I wouldn't leave it that way.
To explain and say it a different way, if you run 2 starter cables to your starter, you don't double the voltage. With two cables you still only get 12 Volts to the starter. But if the starter runs better with 2 then the first one couldn't carry the current your starter needs. Either it was too small a gauge wire or the wire wasn't connected well to the battery.
For your tail light, both the E and I are fixed: 12 Volts and 0.03 Amps for BA9 High Power white. Long story short, if you connect the light to the battery with short fat leads the light with glow as bright as it can on 12 V and draw 0.03 A, (0.4 Watts). But if you reduce the conductivity of the wires by putting a 2 ohm resistor in series, the light will only get 6 V and glow dimmer by maybe half. If you run a jumper wire from the battery to the less bright LED and it suddenly glows brighter, why leave the jumper in? You wouldn't do that with a manifold leak, would you?
I'm guessing you didn't have a good (nearly 0 ohms) connection at the bulbs until you shared a better connection from the other circuit. You didn't change the ground so that brown wire's not the issue. Something is wrong on the supply side. I would find out why the lights are not as bright with the stock wires. Get your meter out and measure the voltage at the light, with the light on, but without the jumper. It has to be less than 12V. Trace back to where it becomes 12 Volts again. Is a 6 ohm resistor in series instead of parallel?