[triffic]

Yes, you can expect them to get hot. Effectively all they do is provide a second path from the 12V positive supply to earth, bypassing the lamp so that BCM "sees" a higher current - so it doesn't trigger the bulb failure warning.

Not sure why the one on the left did not work - perhaps you had not made a good electrical connection, or perhaps the resistor itself is faulty. However, if only one is enough to stop the bulb failure warning then I would go with that. Obviously make sure you mount it onto something that can take the heat and make sure that it's kept away from anything that might be damaged by heat and you should be Ok.