Trying to think of mechanisms

Is there any plausible way to connect solar activity with Earth's climate ? In the visible region of the spectrum, sunspots make only a minor difference in solar output. But in the ultraviolet, a 6% decrease due to no sunspots is significant.

Smog, created by the action of UV on atmospheric pollutants, almost certainly acts as a greenhouse gas. Decreasing the amount of UV would plausibly decrease the amount of smog and hence decrease the amount of greenhouse effect, leading to cooling.

Atmospheric pollutants are sometimes human caused. Sometimes the pollutants are natural in origin, such as, the emission of hydrocarbons by certain kinds of trees. The Great Smokey Mountains are said to have a "smokey" appearance precisely due to tree emissions.

It therefore seems plausible to me that an absence of sunspots could lead to cooling. Detailed calculations are in order (but I'm not going to do it).