First of all Welcome to the forum!
Now lets first establish what scooter as in the engine you have and we'll go from there. So even though it is labeled the YY250T which is supposed to be the vertical cfmoto copy it could be labeled wrong and be the horizontal linhai and here is a picture of both engines;
Now it doesn't matter which one because we have a diagram of both and they are very close to the same.
thescooterprofessor.proboards.com/index.cgi?board=250g&action=display&thread=430It's the first one or if it's the linhai the seconds one. You will also see the differences in the two which are small.
Now lets discuss the CDI, no matter which engine you have the CDI is the same;
So here's the pin out on the CDI;
Black = 12Vdc from battery (this is a DC powered CDI)
Green = ground
Gray/white = engine kill wire
black/yellow = feed to coil
red/white = signal pulse wire from stator
Now there are several things that need to be checked and since you said you give it the old giggle the wire and it started but now it won't that's a dead giveaway so it's a matter of figuring out the gremlin that's causing this BS.
Now you are correct on the black wire having power and it is 12VDc from the key switch when it is on. The key switch is fed from the red wire from the battery that has the 15A fuse. I would remove the harness wrapping that holds the wires to the CDI and pull the plug from the CDI and put my volt meter lead on the black wire and turn the key on. The black wire form the key ignition feeds several things and splits in the harness and the Chinese are famous for using cheap brass crimp connectors to splice the wires. With the key on and volt meter connected move the wires around and see if the voltage goes on and off. If not then move on to the gray/white wire, if it does then you've got to trace it out and find out why.
Now the gray/white wire as mentioned is the engine kill wire and it works by simply grounding out the CDI when the key is off or the engine kill switch is pushed to the off position. If this wire is shorted as you say which would mean it's grounded out then no voltage from the CDI to the coil. This is possible, remember the moving the wires and it started? You got to remember these wires are in the harness all together which includes the green (ground) wire. If it is bare somewhere in the harness and touching the ground then again no power from the CDI to the coil.
Now we can test for this, unplug the gray/white and black 2-plug and take your volt meter, set it to ohms and do the following;
(1) put one volt meter lead to the gray/white wire and the other to ground
(2) turn key on
(3) Check the meter to see if you have continuity or ohms resistance, with the key on and the engine kill switch in the run position you should have no continuity as in no ohms resistance. If you do then you have one of 3 problems;
(A) gray/white wire is shorted out to ground
(B) key switch is bad and not opening the kill circuit with the key on
(C) engine kill switch on handle bars is bad and again not opening the circuit when in the run position.
Now there is also a easy way to check out the gray/white on the CDI to see if it's the problem. When you unplug the 2-plug look at the end of the plug, all these plugs have a little small slot in the end by each wire in the plug. You can take a very small screwdriver and insert it into this slot and it will force the locking ear on the connector to let go and you can remove the wire from the plug. Remove the gray/white wire and then plug the plug back into the CDI with the one black voltage wire still in the plug. I would remove the spark plug and lay it on a grounded spot and turn the engine over to see if you have spark. If so then re-insert the gray/white wire and see if the spark fails, if so then you've got to determine which one of the 3 possibilities it is and fix it.
The reason I say remove the plug is if this is the problem then with the gray/white disconnected you can't kill the scooter with just turning the key off if it started.
Now if these two wires check out then the next wire to check is the green ground wire, if the CDI isn't grounded then no voltage to the coil.
If it is good then the next wire to check in the black/yellow to the coil from the CDI, they are famous for having bad end connectors on the end, I personally soldier all of mine.
That should head you in the right direction and remember we're here to help.
JR