I kind of used a brute force solution, and it’s probably overkill, but it now works.
Backyard_Lights_Switch is a virtual on/off light switch.
Back_Patio-On_Motion-Timer is a 15 minute timer.
Back_Patio_Light_Switch is on a shared patio with Library_Patio_Light_Switch and not physically close to each other (unfortunately).
Back_Patio_Motion_Start:
IF Back_Patio-Motion is Motion and, Time-of-Day is Dark, Backyard_Lights_Switch is not On,
do Back_Patio-On_Motion-Timer action "reset",
do Back_Patio-On_Motion-Timer action "start",
and set Backyard_Lights_Switch On to true.
Back_Patio_Motion_Stop:
IF Back_Patio-On_Motion-Timer is elapsed and, Backyard_Lights_Switch is On,
set Backyard_Lights_Switch On to false,
and do Back_Patio-On_Motion-Timer action "reset".
Backyard_Lights_Off:
IF Backyard_Lights_Switch is not On or, Library_Patio_Light is not on, Back_Patio_Light_Switch is not on,
turn Back_Patio_Light_Switch off,
turn Library_Patio_Light off,
turn Bedroom_Patio_Light off,
do Back_Patio-On_Motion-Timer action "reset",
and set Backyard_Lights_Switch On to false.
Backyard_Lights_On:
IF Backyard_Lights_Switch is On or, Back_Patio_Light_Switch is on, Library_Patio_Light is on,
turn Back_Patio_Light_Switch on,
turn Library_Patio_Light on,
turn Bedroom_Patio_Light on,
and set Backyard_Lights_Switch On to true.
Thank you for the suggestions. It helped resolve my problem.