I wouldn't waste your time. A butt has enough internal fat to keep it moist, and they are typically thick enough that it would take more than overnight for the brine to penetrate.
If you want to get more flavor inside you can inject. Chris Lilly's injection is a good starting point, but most guys cut back on the salt.
3/4 cup apple juice
1/2 cup water
1/2 cup sugar
1/4 cup salt
2 tablespoons Worcestershire
"Ron Rico, Boss. You can call me Captain Ron..."
The Naked Fatty!
FEC-100/BWS Party/Memphis Pro SS/PBC/LBGE X 2/SBGE/Mini BGE/Nomad Pellet-matic/Good-One Model 42/WSM X 2/Cookshack Smokette 008/Weber Performer/Saber Cast 500/Weber Gasser (RIP)/Weber Kettle X 2/Weber Smokey Joe/WGA/UDS/Coffee Roasting Gasser and a pickle
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