To my eyes, it looks like you need more power than the function generator is going to provide.
In fact, I bet the function generator is going to output 1Vpp @ 10mA maximum.
A first thought would be to study the MOC3063TVM datasheet to see at what point it triggers. That is, the working voltage and load current to make it do something useful.
Also, may I suggest that you test the triac using 24VAC from a standard door bell transformer instead of the function generator? The bell transformer will lower 120VAC to 24VAC and make it less deadly to you but still provide enough current to do something.
You could also put an incandescent light bulb in the load side to give you a visual indicator of your circuit function. Either that or a DVM or 'scope.
On the input side, you could rig up a simple switch that applies the proper trigger voltage to the anode through a load resistor. You should tie the cathode to ground in that case.