Hmm, 11 V on the tabs of the defroster is an odd value if the battery is fully charged, which I am assuming.

Sure, Ohm's Law (V=I*R) says there will be a voltage drop in the wiring, but only if current is flowing, i.e. with a functioning defroster grid. Which is not the case. And a 1 V drop would be rather high too.

With a totally broken (open) defroster grid, measured voltage of the tabs MUST equal battery voltage. No current means no voltage drop in the wiring.

If your battery measures, say, 12.5 V, but the defroster grid tabs measure only 11 V, I'd say the high input impedance of your (presumably) digital multimeter enables it to measure a (tiny) leakage current, potentially.

Right now I'd make a testlamp with a 5 W carbulb and see if it lights with one contact on the "hot" tab of the defroster and the other on a good chassis ground somewehere. The lamp should light brightly, and if so, that would mean the supply is coming in strong.
Next step, move the chassis ground of the testlamp to the "cold" tab of the defroster. If the lamp lights brightly again, the return path through the chassis ground is also OK and that would mean the defroster grid is shot.
Given the fact tat continuity of the grid seems fine (but what is its actual resistance?) I'm inclined to expect a problem with either the +12 V supply or the chassis ground return.