CC2640R2F: How to implement BLE pairing behavior with central device like this smoothly?

Hi all,

Customer wants to use CC2640R2F to pair with a central device by following rule:
(1) The first time, DUT (with CC2640) can be discoverable by a central device , but central device is unable to connect the DUT.
      Till DUT's HW button is pressed, a central device can pair (then bonded) & establish BLE connection with that DUT.
(2) Minutes later, the central device disconnects from the DUT for some reason.
      The DUT becomes scannable but cannot be connectable by other central device unless user presses the button.
      A minute later, the central device can re-connect to DUT.

What is the Advertising type needed to set by DUT for each changing status and what action is needed for the central device?

Sincerely,
Jinhua