Can Bray and Eddy Cycles Explain Global Warming?

There's a schematic that is frequently promoted by John Shewchuk on X to claim thatt long-term solar cycles explain much more of temperature variability of the last 2000 years than changes in greenhouse gases like CO2. The implication is also frequently made that the current warming over the last century or so is due to these cycles and not to changes in GHG concentrations. One common version of this graph is here. The Hallstatt-Bray cycle, which has a periodicity of ~2400 years, and the Eddy cycle, which has a periodicity of 976 years, are both related to sunspots, and so they indeed do have an impact on total solar irradiance (TSI), and therefore they can in principle have an effect on global temperatures on millennial timescales. But the significant question is, by how much? Astute observers will note that Shewchuk didn't include any scale for the y-axis; the impact of these cycles could be negligible or large as far as this schematic is concerned. I do find ironic,...