IIRC - Neither Brophy or Mallory claimed the 'Headless Cocking Piece' to be "standard" on model 1899 carbines.
Brophy incorrectly stated that it was only found on Model 1899 carbines.
 
(Although it most commonly is found on some model 1899 carbines, it can also be found on some rifles).

In reality, it was an economy move that proved to be more expensive to manufacture than the 'knob-version' and was discontinued.

It would originally have appeared on only a narrow (serial number) range of model 1898 rifles and model 1899 carbines.

Mallory wrote that the headless cocking piece was the idea of Lt. T. C. Dickson and developed in 1899. It was approved in late April, 1899, and disapproved in October, 1900.

Logic would indicate it to be "correct" only on rifles and carbines made during and slightly after that time period (until inventory was exhausted).

Although, with arsenal refurbishment practices, if the 'headless cocking-pieces' were just treated as a standard component, they could have ended up Krags outside the narrow production period.

FWIW - My 'headless cocking-piece' came off a 'cut-down' model 1898 rifle that was made in 1900.

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