Ok - so the "Front Side Marker Lamp" and the "Cornering Lamp" are in the same housing, but different circuits.
The front side marker lamp is "high resistance" = small bulb (24), low current
The front turn lamp (A) is "low resistance" = big bulb (2057A), high current
The front park lamp (B) is "high resistance" = small bulb (2057A), low current
When the headlights are off and a turn signal is on, power comes down the blue wire (light blue for Left, dark blue for Right) and powers both the Front Side Marker Lamp and the Front Turn Lamp.
The Front Turn Lamp has a direct path to ground so it lights up when powered by the flasher.
The Front Side Marker Lamp grounds through the other two front park lamps filaments so it lights up at the same time as the front turn lamp. Current flows from B to A on the front side marker lamp when it's lit.
When the headlights are on, all the parking and marker lamps are lit by the grey/black wire from the headlight switch. Current flows from A to B on the front side marker lamp and is grounded through the Front Turn Lamp bulb filament. When a turn signal is turned on, there is now power on both sides of the Front Turn Lamp which shuts it off when the front turn lamp is lit so the two lights alternate, when one is on, the other is off.
So, current flows both from A to B and from B to A in the Front Side Marker Lamp depending on if the headlights are on or off. For this reason, most LED's won't work since LED's are designed to be polarity sensitive - it'll work one way, but not the other.
Rumor has it that there are LED's on the market that are bi-polar and would work in this application, however you also have to consider the front park lamps are providing ground so if those are swapped with LED's, they might light when you don't want them to or not at all.
Hope this helps explain how this circuit works and why.
Personally, I'd put in some long life 24's