Want to switch my light fixtures to 12v and use LEDs

So I have all the original light fixtures for my caravan, and as I've been tearing it apart, I've discovered that the 110 needs to be rewired (it worked, but my god am I glad I didn't try and use it! - pics to follow).  Since this guy will almost always be boondocking, I'm seriously considering not reinstating, and rewiring him for all 12v.

All my reading has said that to use the fixtures in a 12v system, I just need to wire them in, and use a 12v bulb.  But the 12v LED bulbs I'm finding have a different base.  Are my search skills just weak, and they're out there, or do I need to rewrite these with a different base?  If so, where do I find these?

Thanks!