I voted for take the job and keep looking, and I quoted this because I’m curious why it’s deceitful to keep looking? A job isn’t like a relationship, businesses fully expect that people have career ambitions and will be taking steps to further their careers, which is exactly why they will say stuff, true or not, about opportunities for advancement. But like a relationship, depending on the laws in your state, it’s generally a mutually understood and beneficial relationship and if it stops being that for one of you, that party can end it.
Of course, I don’t know your qualifications or those of the job, but presumably they have some understanding that the job isn’t ideal for you, perhaps part of the reason they talk about advancement, but they wouldn’t make the offer to you without considering the risk that you take the job and find a better one and leave after a few months. This is why things like “overqualified” come up, because they feel like the job is so below that person that the risk of that person leaving in short order or at least being unmotivated isn’t worth it. So, unless you blew smoke up their ass about how it’s your dream job, I don’t think there’s any deceit on your side.
That said, depending on your field, there could be some other issues to consider. As someone mentioned, there could be some complications related to unemployment, if you’re receiving that. Similarly, I know that seeing short terms of employment or long terms of unemployment on someone’s work history are looked upon with scrutiny. So, if you take this and start looking, someone might be curious why you’re already looking and be concerned you’d do the same to them if they offer you a job. On the other hand, if you turn it down, I don’t know what your prospects are, but it might be weeks or months before you find another job, and then you have the latter problem.
On further thought, you could just kind of compromise a bit. Perhaps take the job, see how it goes and try to make it work and take a breath from the job search, but use your time to bolster your resume and get it back out there in a few months. If things work out, awesome, if it’s miserable, you’re still not any worse off than if you turned it down and lived off you’re savings, and if you find something you like more in the meantime, even better. Still, doesn’t sound like an easy decision.