There's no doubt whatsoever that carotid sinus stimulation, even on just one of the carotid sinuses, can cause instantaneous syncope (collapsing, fainting) in humans - and horses. And it's not at all uncommon. But that's to do with a (temporary) loss of consciousness. Not instantaneous death.
(I don't think it would make much difference at all to the outcome if both carotis sinuses are stimulated rather than just the one. It may be that it makes it more likely that the human (or horse) might collapse/faint. I certainly don't think it makes it any more likely that the human (or horse) will actually die.)
'But that's to do with a (temporary) loss of consciousness. Not instantaneous death'
And again your wrong from Bernard Knight third edition.
"It is a matter of some dispute as to whether this reflex can cause immediate cardiac arrest or whether there has to be a period of marked slowing of the heart with negligible cardiac output – or whether an arrhythmia such as ventricular fibrillation precedes such an arrest. Probably any combination can occur, but it is an indisputable fact that collapse and apparent death can occur immediately on the application of pressure to the neck."
The dispute of course is not with you as you are not a internationally recognized pathologist or probably even an mma fighter. Though to help you, that last sentence would be well worth trying to get your head around. Particularly this part That it is 'an indisputable fact that collapse and apparent death can occur immediately on the application of pressure to the neck.'
I know who at least 1 of the 2 imminent pathologists who disputed the point made by Knight and Gonzales as to the cause - but that does not detract from the recognition of 'immediate death' which you continually fail to grasp.