Would a new star slowly begin to brighten or would it be like flipping on a light switch?
Due to the masses and processed involved, there would be a gradual change in the star output from the time of its initial "ignition".
While the first thermonuclear combination "igniting" a star might be an instantaneous event, the stabilization of the star would take much more time. It would involve changes to the whole mass/volume/energy in the system, and thus would exhibit changes in observable states until a stable status was achieved.
Good, short history and a link to further discussion video: