What type of heating system do you have?
IS it gas, electric, heat pump, what???????
I used to work for my dad who has a heating and a/c company, so i learned alot from him.
The "aux" light could be refering to an emergency heating device to help maintain temperature in your home. It helps out the primary heating system, when it fails to keep up with demand.
The noise should be checked, I have a feeling it is trying to come on but is not able to, and that is what is causing the noise. The light could be flashing to signal it is trying to come on but goes off when it fails to come on.
If this is the first time this is happened , is it colder than usual?
might be too cold for your present heating system, just a theory though.
recommend you get it checked out!