So Crypto clued in that all the encounters that give Arsonist Observations also give Perception XP. I should have realized that was the key because it gives the effect down with the XP reward. It looks it gives the effect any time you gain Perc XP with the additional condition that it gives does not give the effect if [XP gained + 1 < current turns of the effect].
Arsonist Observations (5) -> Use medical tears -> 2 XP
Arsonist Observations (4) -> Use medical tears -> 2 XP
Arsonist Observations (3) -> Use medical tears -> 2 XP, 10 energy
Arsonist Observations (7) -> Use chloroauric acid (use 1 energy) -> 4 XP
Arsonist Observations (6) -> Use chloroauric acid (use 1 energy) -> 4 XP, 10 energy
Items and encounters that use energy seem to subtract energy first.