Thank you for your patience, the following is the response from our engineering department:
The external 12-19 V DC jack is the primary power input connector of Intel NUC Board D54250WYB and Intel NUC Board D34010WYB. However, the board also provides an internal 1 x 2 power connector that can be used in custom-developed systems that have an internal power supply. The internal 1 x 2 power connector is a Molex 5566-2 header which accepts a Molex 5557-02R connector from the power supply.
There is no isolation circuitry between the external 12-19 V DC jack and the internal 1 x 2 power connector. It is the system integrator’s responsibility to ensure no more than one power supply unit is or can be attached to the board at any time and to ensure the external 12-19 V DC jack is covered if the internal 1 x 2 power connector is to be used. Simultaneous connection of both external and internal power supply units could result in potential damage to the board, power supplies, or other hardware.
There’s nothing special required to use the internal one. Should just work. At this point, engineering will need the model number and specifications about the PSU you are trying to use on the internal header.