Electric parts tend not to burn (and thus smell) that long. My guess is something touches the heating element (loosend part or rodent). I’d open it up to check the inside. If you are not confortable doing that, get someone to do it.

It’s been an issue for two months which might cause one to think it’s not urgent, but an oven usually isn’t daily use. Just check it asap you don’t wanna risk a fire (not saying it will burn, but it’s a risk)