Woody,
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What is in that little black box? If I failed to ground it correctly, could I have fried it?
It's probably a rectifier diode or diode bridge, along with a high-wattage Zener diode and resistor. If it's properly designed, I don't think a disconnected/misconnected ground would fry anything.
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If I read the wire diagram right, the yellow wire Y's into the headlight hot wire...
Here's how I read it:
1) Connect the red wire to the rectifier output wire (rectifier is removed).
2) Connect one green wire to the rectifier input.
3) Connect the yellow wire to the lighting coil output.
4) Connect the other green wire to frame ground.
I don't know what's up with the two green wires. A continuity check would tell you if they're connected together.
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how do I know if the bulb is going to blow, until it does?
Remove the bulb and check the voltage. It's OK to see a bit more voltage than the bulb rating as it will probably drop a little under load, but 35V on a 6V lamp will blow it in a spectacular fashion.

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And if the bulb blows, and I am running the original resistor, how do I keep that from going up in smoke as well?
A voltage check will work here too, as will a finger heat check on the resistor (warm to very warm is OK, burning hot is not). Power resistors are pretty rugged if they're rated properly for the job they have to do.
Have you gone over the entire wiring harness carefully? If the MT125 is anything like the MT250 - as I assume it is - there's a ton of wires, connectors, switches, bulbs, etc., any of which could mess you up if connected wrong.
Ray