That's a large crack in the tank. I would suggest seeing about replacing it, especially as it appears to be fairly accessible without taking the entire motorhome apart. That isn't always the case. A plastic fabricator may be able to patch it up, though, if you decide to go that route. If it's brittle with age, it probably would crack again. I honestly don't know how prone (if at all) ABS is to getting brittle or crumbly.
The light socket looks to be in very poor condition. Even if you get it working, I suspect it would not be reliable. The upper of the two base contacts is loose from the plastic mount, for one thing, and the lower right corner looks almost as though it has been burnt (though that may just be accumulated cruft). At any rate, I think replacing these lights would be much less trouble in the long term than trying to figure out why they aren't working now and getting them usable.
I must say on the whole this looks remarkably clean and solid for something that's about forty years old.
