So, I found a wiring schematic for the Baja 250/Gio X31 from another group, and got it all working. The piece I didn't realize was the brake switch, which needs to be depressed when cranking the engine. As soon as I wired that up, it fired right up.
For reference, I'm posting the wiring diagram for future archival purposes as I found it invaluable in getting it all working, along with everyone's help.
Thanks again!