Ok I've managed to figure this out. I'll detail the issue here in case other newbies like me come across this.
There are 2 ways to trigger events in animations in Unity, using the Animation Window (Ctrl + 6) or if you select an FBX file with embedded animations.
Animation:
If you add an event to the timeline and see no functions listed, make sure you only have one FSM on the GameObject. Having more than one will cause the list to be empty.
It should look like this...
FBX:
Select the animations tab in the FBX, then select the animation from the clips list...
Go down and expand Events, then in the preview window scroll along the timeline to where you want the event, click add event. Type SendEvent into the function, then type the name of the transition event in your FSM.