Hi Nev
Drawing 'A' is the correct way to wire your LED strips. This is referred to as a parallel circuit, and as such, both lights have the full 12V across them (this holds true for however many lights are connected across the battery in parallel).
Sketch B shows two LED strips wired across the battery in series, and in this configuration each light will have just half the battery voltage across it. If these were ordinary incandescent bulbs, each one would glow at half brightness - but being LEDs they probably wouldn't glow at all.
(Christmas tree lights (the incandescent type) are wired in series, so with 24 x 10V incandescent lamps connected across the 240V mains, each lamp will receive (drop) 10 Volts).
A switch may be more convenient than connecting and disconnecting them from the battery, but isn't strictly necessary.
An inline fuse wired close to the battery would be a good idea. If you're only using two of those strips, a 1A fuse would be suitable.