I don’t know details of automobile light bulbs, but I’d be surprised if you get near-zero light from 11 volts. (BTW, I presume you are measuring with the light bulb in place. If it’s 11 volts open circuit, then it’s whole 'nother problem.) That said, …
Rather than “high resistance short-to-ground in the line feeding the subject light”, more likely a high resistance connection in that line. Maybe you are very lucky, and the high resistance is just in the contacts of the relay that feeds that light. Try replacing the relay (swap with an identical one if the car happens to have it). If replacing/swapping works, try the old one again to see if the problem was in the socket, rather than in the relay’s internal contacts.
(If this light is fed from a separate fuse, try swapping that fuse to see if it has a “soft” failure or if its socket contacts are the problem.)
If it’s not the relay (or the fuse contacts), you will probably need the wiring diagram to follow “12V” from the battery, through the fuse box, up to the lamp socket. If you are lucky, the high resistance will be between contacts in a connector, and you can fix it just by unplugging and re-plugging the connector. If you are not lucky, the high resistance will be in a crimp connection or – ugh!! – a flaw in a connector or wire itself.
If the problem is a flaky connection that gets fixed by unplug and re-plug – the relay, fuse, or harness plugs – maybe put on a bit of dielectric grease on it.