It's been 4 years since the last comment, but I was running the quest today and it appears to be a triggered proximity spawn now. Once you enter the room while on the quest, he pops at you.
Went to the basement - billy popped. Cleared games room twice and no billy. Zoned in and billy instantly repopped with the games room PHs. Cleared chapel 3 times. Third time killed the named but didnt talk to the npc, zoned in and Billy popped on his own in the chapel.
Total only like 20 mins when whole of nek castle is grey.
Often times Billy will be up when you zone into the castle. I never tried this but heard if he is not up, leaving and re-entering the zone (provided you have not begun the lockets quest) may make him spawn for you.