I can't locate it now, but a research study was done to determine the response time of desaturations to respiratory interruption.
To the best of my recollection something like 30 healthy adults were monitored for oxygen saturation while awake for several minutes sufficient to establish a base line.
Each subject was told to hold their breath for as long as possible, while oximeter readings were recorded each second.
IIRC, the oxygen saturation dropped (on average) approximately 16 seconds after breathing ceased (I honestly don't remember if the threshold was a 3% desaturation or 4%)
That sets up an interesting question: IF the brain reacts (is aroused) by a low blood oxygen level (caused by apnea), but the blood oxygen level is slow to respond to the apnea, there is some period time that passes before the brain reacts to an apnea*
I've found it interesting, in observing my own oximeter recording that very often my oximeter might record a 3% desaturation that takes 1-2 seconds to drop from a steady baseline. (At first I thought that these might be artifacts) But then the recovery to return to baseline would take 10 seconds or more. (I suspect if the initial drop were actually a "positional" or "contact" artifact, then the restoration back to baseline should also be abrupt -
* as different from the brain reacting to excess CO2.
UPDATE: Just found similar information on "Emergency Medicine Update" website where they demonstrated "pulse-ox lag" to breathing.
Here the physician begins with a 100% O2 and STARTS by holding his breath.
After 37 seconds the O2 level BEGINS to drop.