I agree with the brake pad diagnosis. Some pads have a metal insert which is designed to rub against the brake disc when the pads wear down. This produces a screeching sound which supposedly alerts you to the need to replace the pads. I've never had these but it seems reasonable to assume they could screech a little when not braking, screech more when braking gently, then not screech at all when braking hard. I don't know why there would be no sound when cornering. Does anyone have experience of this type of brake pad?