The is no actual abrupt doubling of the CO2 level, which is why ECS is not a good measure of how our climate will respond to increases in CO2 level.
All the definitions of ECS ether specify a time frame of instant/abrupt, or do not specify a time frame.
The definitions that do not specify a time frame of the doubling time, can only be abrupt, because any other time (not specified) would be too subjective.
What do I mean by this? A definition of ECS without a timeframe for the doubling, would leave the question open,
did the doubling occur in one year, ten years, ten thousand years, the different answers would matter, unless the time frame was always abrupt,
and so well understood, that it did not need to be mentioned.