Sounds like it could be a bad ground. You should have B+ (~12v) at the one side, not 6v. Here's some info that might help with your diagnostics:
Heated Back Window Grid Wire Test
1. Using a strong light inside vehicle, visually inspect wire grid from outside. A broken grid wire will appear as a brown spot.
2. Run engine at idle. Set heated back window switch and light to ON. The indicator light should come on.
3. Working inside vehicle with a DC voltmeter, touch the probes to the broad red-brown strips on sides of back window glass. The meter should read 10-13 volts. A lower voltage reading indicates a loose ground wire (pigtail) connection at grounded side of back window glass.
4. Contact a good ground point with negative lead of meter. The voltage reading should not change.
5. With negative lead of the meter grounded, touch each grid line of heated back window glass at its midpoint with positive lead. A reading of approximately 6 volts indicates that the line is good. A reading of zero volt indicates that the line is broken between midpoint and the positive side of the grid line. A reading of 12 volts indicates that the circuit is broken between midpoint of grid line and ground.