I also have a stong but unconscious tendency to adjust my accent to someone I am talking to
That's me, too. A forces childhood moving from posting to posting has left me with largely RP, but when I'm talking to local folks, I do tend to drift into Black Country. Proud of it, too!
Btw, Black Country is a dialect, not an accent as such, with roots in Anglo Saxon. For example as in the local greeting, 'Aer bist, aer kid?' 'Bist' being the second person singular of the verb 'to be' in modern day German... IYSWIM.
Mind you, speaking with an Australian once in the course of my job, I found myself sliding into Aussie twang, couldn't stop. In the end I made an excuse and took a break to get my own voice back. Empathy can have an unforeseen downside 