Ok, there is your problem. The pins 1, 13 and 14 are not powered.
Run one side of the 110V to pin 13.
Now hook one wire from a neon to pin 1 - that is alarm1.
Take the other wire from that neon to the other side of the 110V.
circuit complete.
do the same for alarm2 only use pin 14 instead of pin 1.