Sorry to belabour this - just attempt to explain further
With the traditional incandescent indicator lamp, the circuit looks like below:
You can see that when left side is selected, current flows in parallel path to both the left-front and left-rear turn signals;
but also connects in another parallel path, which is through the indicator lamp and THEN through the two right-side lamps (in parallel) to ground.
The reason that the indicator lamp lights, but the right side turns do not, is because the resistance of the small low wattage indicator lamp is >> (very much greater) than the two incandescent turn signal lamps in parallel. So the applied voltage gets 'divided' between the indicator lamp and the two opposite side turns, but is not divided equally because of that resistance difference. So the voltage across the indicator lamp is much larger, sufficient to illuminate it, while the turns stay off (even though there is actually current flowing through them) i.e. X V >> Y V
Now - when you change to LED turns, things change quite dramatically - LEDs have very high resistance compared to a bulb (even a small wattage one) which is why they draw very low current. Now, when you look at the equivalent circuit above, since the opposite-side Turn signals now have very high resistance compared to the indicator, most of the voltage will be developed across those
i.e. Y V >> X V - so now it is the opposite side turns that light instead of the indicator.
The result is that
both sides will flash - like emergency flashers - regardless of which side is selected by the switch.
Now - if you simply replace the incandescent lamp with a non-polarized LED (current flows in either direction)* then you STILL get a voltage divider situation between the Indicator lamp and the Turns - so you will most likely still get the opposite side turns at least glowing.
The way to resolve is to install a couple of diodes to isolate each side from the other.
The diode allows current to flow forward through it, but not in reverse (same as LED, which is just a diode which gives off light).
So while the one diode allows the indicator be in parallel circuit, the other diode blocks the current from flowing through the opposite side Turns. And of course each diode performs the opposite function when other side is selected by switch
* There is no such thing as a bi-polar LED - included in the LED packaging are conventional diodes which are connected such that regardless of the polarity of the applied voltage, the positive is always routed to the anode of the LED. It can also be simply two LEDs connected in parallel in opposite polarities such that it either conducts through one or the other.
Some general notes:
A low wattage bulb (indicator lamp) has higher resistance than a high wattage turn signal lamp
Two turn signal lamps in parallel have half the resistance of a single turn signal lamp.
So Indicator lamp has >> (very much greater) resistance than two Turn Lamps in parallel.
An LED has >> resistance than an incandescent lamp and draws << current.