Informal enquiries for faculty position
If you’re going to send such an email, I suggest you make it short and direct it to either someone you know or someone in your research area. (Hence this advice is mainly for research universities.)

You can introduce yourself, say you’re applying, and mention that you’re excited about this job.  Taking the extra effort might show that you’re serious, but I honestly find that it rarely helps and can even hurt in the case of a lengthy letter to a busy department chair.

I think if you know someone in the department, that’s when it’s probably most effective; e.g. an email can alert them to your application so they can mention you to the hiring committee, even if they’re not on it this year.