If they are wired in series (doubtful) you would have 3 volts available at each fixture. More likely, they are 12V wired in a "daisy chain", 12v passed from one fixture to the next and the common ground may be at one point. Measure voltage available at each fixture.
These types of problems are typically associated with a poor ground. The electricity (12V) needs a good path between battery positive and battery ground. Investigate ground potential by measuring with metered resistance between your light's ground location and a clean piece of frame or directly to battery (-) post.