Hey there!
Thought about this for a moment, and came to the conclusion that I wouldn't over-engineer it.
In my opinion, both Brindlewood Bay and this Adventure in particular lend themselves to good 2 player play. There's not a lot to "balance" around, and while player-interactions are always great to make it more interesting, they're not an integral part of Brindlewood Bay.
Some additional advice:
- Remember that failed rolls progress the story, albeit with some personal risks attached. As you will only have one player, expect them to fail things they're just not skilled at. But don't let that keep you from progressing
- Make use of the crowns to reverse bad outcomes, as outlined in the rules. This will help you keep it interesting without killing your player character
- Let your player paint the scene. Use more rather than fewer of these questions. This will give you more to work with, the occasional break you might need for thinking and keep the player invested
- While I'm not a fan of DMPCs, I'd let Dalrymple force the player to take a rookie deputy along with them. Or a reporter, or something. He shouldn't be all too useful, but is a great tool for you to hint things towards your player. Not in terms of mechanical hints, but as a slight nudge and guide toward certain actions. "Dalrymple always says to look for enemies of the victim first!" or "Didn't Amelia tell us to ask Mr. Glooms former colleague about this?"
Hope these help! Let me know how it went :)