After pairing RuuviTag with a mobile phone, I would like that it is not visible for further BT scans. Is that possible? I know that e.g. mobile phones can set discoverability to off.
RuuviTag is not visible to other devices while the connection is ongoing, but it will become visible once again after the connection is lost. If the RuuviTag would not restart advertising after disconnection no device could not connect to it anymore.
As I have understood, pairing means registering the connection information (the pin code etc.). The actual connection can be made if you have paired the device once. I suppose that RuuviTag does not need to advertise if the mobile phone has the pairing information. So the phone can reconnect.
Pairing security-wise is a bit different from establishing a connection. The tag needs to advertise so that the phone can initiate a new connection later on, even if they use the bonding information from a previous connection.
It probably would be possible to write a firmware which uses directed advertising to advertise itself only to a previously connected phone and it might now show up on other phones by default, but a dedicated scanner would still be able to detect the directed advertisements.