wrote:
IE: Is it possible to have an on/off star?

Potentially yes if the mass is too low to initiate full main sequence
powering fusion between the most common isotope of hydrogen, but
justenough (around 10^6 K) to slowly burn off the low mass elements
like deuterium, lithium, beryllium and boron.

If the core temperature gets to 10^7 K or higher then it will almost
certainly become a main sequence star, but if the mass is insufficent
it may only manage to burn off the easy fuels without ever fully
igniting the main sequence hydrogen burning reaction.

I don't know if any stars in this category have been observed. They
would be rather small and dim even during their brief active stage.

...Or does the mass have to
surpass the necessary requirements, such that once fusion commences, it
would be guaranteed to be ongoing. ...And 2): would the critical mass
ensure that the ignition would initially commence with the very central
atom within the mass, or can fusion commence within a plus or minus
gravitational pressure range? ...Jon

It is a soft start. Once the pressure and temperature are almost enough
some lucky collisions will result in fusion. Reaction rates then
increase rapidly with temperature.

Regards,
Martin Brown