The high frequency angle says a lot. I'd say this will be an issue with whatever device is driving the output to the indicators.
You are almost certainly hearing PWM (Pulse-Width Modulation) whine, there will be a computer or PDM performing this electronically. It is a high frequency modulation, and it can cause the solid state components to vibrate at that frequency, which is what you are hearing.
With modern LED lamps, if you just hook them up to a voltage source, they will short-circuit and blow up. If you had a car that originally didn't come with LEDs, and you convert it, then you get bulbs that have resistors (ballasts) in them, which basically put the current flow in a chokehold to eliminate the short circuit problem. However, this approach means you don't fully realise the energy efficiency of LEDs. So, on modern cars designed for LED illumination, manufacturers use a computer to digitally switch the LED on and off thousands of times a second. As a result, "on average", the LED receives the correct amount of power, and no ballast is required.
This is also why when you see videos of modern cars, often the lights are flickering on the video footage, even though they look normal to the naked eye.
