Display Layout (from behind, left to right) A12345 B12345 C12345 D12345 E12345 F12345 (Z123) G12345 Connection Blocks (mapping) B1 F1 A2 G2 | E3 B4 F4 A5 A1 G1 D1 F2 | F3 A4 E4 B5 Z3 C1 E1 E2 | G3 D3 D4 C5 Z2 Z1 B2 D2 | C3 C4 E5 G5 Z1 Z1 C2 A3 | B3 G4 D5 F5
I traced the connection block pins to the corresponding display dots. There are 3 traces which interact with the reed switch, these are to the far left when looking at the back of the display, which I've labeled as "Z".
Directly applying voltage to a single dot with a standard 5 volt USB power source, a single dot can flip. Reversing the polarity will cause the dot to flip back to the other state.
Pretty beat up, but still decent looking. Hope you can bring it back to life - love flip dots!