As a commentator pointed out: the Younger Dryas Stadial (a sharp ‘kink’ in temperature that happened some 10,000 years BC, or 12,000 BP) is clearly visible in the data.
The YDS is thought to have occurred as the North American Ice Sheets collapsed, causing a sharp reversal in the general warming trend after the end of the Ice Age 20,000 BP.
In essence the temperature goes up, then down, then up. The CO2 follows temperature as it goes up, but its reaction time lags temperature in a smeared response some 800 years long. So as temperature sharply reverses and reaches a low 800 years through the 1500 years of the YDS, the CO2 stays flat for the whole 1500 years.
So: pretty evident that CO2 follows temperature.
I forgot to mention: The Younger Dryas temperature change was not completely global: in particular Antarctica would have missed it.
But the CO2 change WAS global thanks to excellent mixing. So a CO2 signal from ice from Antarctica shouldn’t be uncritically compared against an Antarctica temperature proxy. Compare the CO2 behaviour against as many global temperature proxies as possible.