I do hope your cylinders are not Nikasil ...
As per the alternator, if the light stays on it is because it is not making electricity.
For it to produce electricity i needs a proper excitation provided by the rotor. ---> check if it is open or shorted using an ohm meter.
The rotor properly energized make a huge magnetic field in rotation because it is bolted to the motor. This induce current in the 3 coils of the stator. ----> check that they are not open circuit or shorted (they are very low in resistance, 0.3~0.6 Ohm, so you need a proper ohm meter to check them. Check two wires at a time. 3 measurements total. The actual value is not relevant, it should nbe the same on the 3 measurements. If not, you have one winding partially shorted by insulation failure due to oil or solvent pollution.
If both tests are correct, you can start the engine and measure voltage produced by the alternator ----> measure ALTERNATIVE voltage two wires at a time on the stator. You should get something like 8 to 20 V and more AC depending of engine RPM. (*)
If everything is fine, you have proved that the alternator is making it's job : producing electricity. But in AC. Your bike needs DC to run. So you have to check the diode board. You'll find a test procedure to test the set of "positive" diodes and "negative" diodes. Do not forget the little ones. If the diode board is toast, you can either replace it or fix it.
If all tests are good, check the big red wire coming out of the diode board and going to the starter motor : it should be plugged on the same post as the big red wire from the battery....
All these test are longer to describe than to make. Write them down on a piece of paper and mark them "check" once done. In a check list way. Simple and effective.
I hope this helps.
* : measure the output voltage of the stator with engine running at the diode board end. This will also check the connecting wires. If you are unsure about your regulator, you can wire jump it to check the voltage. And reduce the time the engine runs with the regulator jumped.