The current required for the LED's is minimal, so I am guessing that AWG 18 or 20 would be fine. But, in an RV another consideration is the mechanical strength of connections, etc., therefore, I use 14 AWG in almost all the applications except for the final two inches attaching to the LED, in which case to an LED strip i use 20 or 22 AWG as it solders with much less heat, avoiding damage to the LED strip.
Another thing to remember, to avoid mechanical damage from chafing, sharp edges, etc., I place my wires in a loom in most case, and/or protect from specific image as they pass through hoes, etc. An example, when I installed the feed for a third puck light in my bathroom, the entire two wire connection was covered in shrink tubing.
, on Flickr
Note, the third puck was changed to the same color as the other two post installation.
Here is a photo of the LED strips in my closets on each side of the bed.
, on Flickr
Note, the 20 AWG wires soldered to the LED strips have been contained in shrink wrap tubing. I sue this for almost any place where a mechanical issue may exist, and in an RV, this is virtually everywhere.