Does it also have ground? Easy to forget that one!
Drawings show the yellow wires labeled NM as 12V and the white wire PM as ground and you do need both to make a full circuit!
But then LED are fussy in one way as the polarity has to be correct! Are these tubes that you can put them in the socket the wrong way? Perhaps try turning them over for battery and ground?
Not knowing how the bulbs are built leaves us guessing but maybe even try flipping them end for end might get it?
But first it has to have both battery and ground! But that gets tricky on this one!
I marked it up as I see it being done.
Click this snip for best view!
It looks like ALL three bulbs have to be in and good to make ANY of them work!
Bat. in on red line from switch to first light, then orange out to other lights. That leaves no ground on first light until the other light has a complete path to connect back to ground!
I might start with checking the red path to and through the first galley light, Then look for it as it goes in the others and out on the blue line I've marked up! Those are not wire colors but what I picked to show the different uses!
Do you also have a "front ceiling lamp switch" as well, not shown on this sheet?
NOTE!
This looks like a tricky one!