Thanks for the feedback guys. Additional observations I've made:
1) 34E wire has 12v with ignition key on and 0v with ignition key off when it is disconnected from solenoid. (Which is my understanding of what is supposed to happen.).
2) With all wire hooked up to solenoid and solenoid energized when it shouldn't be, I can get solenoid to turn off by removed 34E wire. (34E has 12 volts when connected to solenoid after cycling key on then back off)
12 volt electrical bay
Close up of connected solenoid (old solenoid)
Schematic (solenoid is item #15)