I'm not sure how hard this is to add to the SAT solver. The formal definition is something like "if for some set of maybe-squares S, no matter what the solutions are to all of the squares outside S, the set of solutions to S is the same, then allow clicking anywhere in S". But that's a combinatorial explosion: just the number of sets S to consider is a factor of 2^#{maybe-squares} . I don't know enough to say if that can be optimized into something sane so that it can be rigorously applied, but a handful of special cases for small unconnected sections of the board would cover most of it.
