Using the MouseArea, one can emit signals clicked, released and so on, but not pressed:

MouseArea {
  id: mouseArea
}

MouseArea {
  onClicked: {
    mouseArea.clicked(mouse);  // OK
    mouseArea.released(mouse); // OK
    mouseArea.pressed(mouse);  // NOT OK: "TypeError: Result of expression 'innerMouseArea.pressed' [false] is not a function."
  }
}

"pressed" is already a read-only boolean, so there is no way to connect or fire a pressed signal in QML.

PS: This seems to be related, but has been fixed for a long time, which is a shame for the current behavior