The observed association of brightness change with magnetic change over nearly two decades is the basis for thinking that changes in the sun's brightness occur over many decades, along with recorded changes in magnetism. If significant, brightness changes over decades could drive non-trivial global temperature change. The climate record indicates a solar influence of this kind. The two curves are highly correlated over several centuries. Those changes in the sun's magnetism may track changes in the sun's brightness, for which direct measurements are lacking.
Additional evidence points to the sun's signature in the climate record over many millennia.
Every few centuries the sun's magnetism weakens to low levels sustained for several decades. An example is the magnetic low circa 1640 - 1720, when sunspots were rare and the sun's magnetic field weak. That period coincided with a climate cooling called the Little Ice Age, when the global temperature is estimated to have been roughly 1 C colder than today. The reason that the isotope records yield information on the sun's magnetism is as follows. Cosmic rays, energetic particles from the debris of nearby supernova explosions tens of millions of years ago, interact with the magnetic fields of the sun and earth and the earth's atmosphere and ultimately can form 14 C and 10 Be.