Ok. You have several options depending on what you find from here.
The OEM KN25 has one stator part number for USA scooters. The GY6 clones have 8 different stators available. They range fron 6 pole to 12 pole, and come in AC, and DC versions. So you have potentially 15 wrong stators, and one correct one.
On ther original engine... Did the light come on ONLY when the engine was running? That is the usual, and makes the light circuit an AC fired circuit. You can find the power feed to the light switch, disconnect it from the stator, and create a new DC circuit. The dis advantage is battery drain, and peak loading your stator.
You may not actually be charging your battery at the moment anyway because even tho the harnesses connect the wiring config is different.
There is one MAYBE here. Maybe you have the correct stator type/size in the new engine, and your bulb is blown. 16 to one shot but maybe
The real cure is swapping out the OEM, and the GY6 stators. parts for scooters . com sells a stator puller for about 20.00 shipped.