Side indicator light stays on even when the car is turned off

[SamW]

One night when coming home I noticed the passenger side indicator light was on, even when the car was turned off. The side indicator doesn't blink even when using the indicator light, just a continuous light. For now I have just removed the bulb to not let it drain the battery. Also tested with a brand new bulb but that didn't have any effect.

I read that issues like these can sometimes occur with a faulty light control module. Also, electronics are really not my strong suit but could a faulty indicator stalk be causing this?

Not sure if even related to this, but the driver side front park light has been a bit problematic for a while now. When turning the car and lights on, it first illuminates as the other side, but then starts blinking and then usually turns off. The light itself also seems to be not as bright as the passenger side.

Anything else to check or is there a way to pinpoint the cause or verify that the LCM is faulty or should I just start sourcing for a used LCM?