Brett partridge could very well be the son of bret stiles also with the "tiger, tiger" notice that "BRETT" has 2 "TT" in it. also the meaning of the name brett is:

Brett derives from a Middle English surname meaning "a Breton",
referring to an inhabitant of Brittany. Brett is both a "masculine and a
feminine" given name.

I believe brett is well and alive, what better way to go off the radar so to speak then to stage his death? also if he did want Pj to believe he is dead he would need a witness hence Lisbon. Also notice that The pigeons had cages in that very room that was opened they didnt just fly in there by the looks of it that house is abanoned, now ask yourself why would someone bring in pigeons?? perhaps the blood used to draw on lisbons face was that of the pigeons?

Just my take on things