Possessed brake lights

[Poptom]

Hi there. First post!
I have a 2007 Toyota Yaris. If the ignition is turned 'off', the brake lights work normally. However, if the ignition is turned 'on', the brake lights are on constantly (albeit a dimmer version of their normal self). Pressing the brake then brightens the brake lights. The same applies to when the engine is running. Once the engine/ignition is turned 'off', it takes the brake lights approximately 6 seconds to turn off completely.
I have changed what I think is a relay unit which I believe controls a multitude of things including fuel injection system, horn and brake lights. The relay in question is a long (column like) relay with three fuses plugged into the top of it, located in the fuse box under the bonnet/hood. Changing the relay hasn't changed anything :(
Any help would be greatly appreciated.
Thanks