Start at the edges
No arm may point off the board, which fixes a lot. A straight piece on the edge must run along it. A junction with three arms on the edge must turn its missing side toward the edge. A corner piece in a corner of the board has only one possible direction.
Work around the border first. Every stone you fix there limits its inward neighbors.
“The border is your scaffolding. Fix it first and build inward.”
Juno
Match or block every side
Each side of a stone either connects to its neighbor or it does not, and both stones must agree. Once you know a side is open, the neighbor must have an arm pointing back; once you know it is closed, the neighbor must not. Keep track of sides you have decided rather than stones you have turned, and the deductions chain across the board.
Endpoints and isolated groups
Endpoints have one arm. Two endpoints facing each other would form a tiny circuit cut off from the star, so they can never point at each other. More generally, any group of stones that closes up without reaching the star is wrong, however neat it looks.
When you have two choices for a stone and one of them would close off a small group, take the other.
Trace the power
Near the end, follow the circuit out from the star and see which runes are not reached yet. The missing connection is usually a single stone that can turn to bridge two groups. If several stones could do it, look at which choice leaves no arm pointing at a wall.