Neither the cigarette lighter next to the gear shift, or the one in the center console will power up. The fuse I pulled looks fine, but I tried replacing it anyway, which did not make any difference. I tested both outlets with a multimeter after I powered the car on, and got 0 V on both.

Is there anything else obvious I should try, short of somehow replacing the sockets? It seems there must be a root cause, since both are non-functional.

 

Something you might try,
Verify with your meter, do you have power on both sides of the cigar lighter fuse, ?

 

I did try replacing the fuse altogether, with no difference. Do you mean continuity in the slot where the fuse goes?

 

We are trying to verify if power is available at the panel that supplies power through the fuse, does the key have to be on to get power there ?

Did you check if any fuses are in the engine compartment fuse panel?