how desire for cessation, never to be reborn, is different from desire for non-being? The Second Noble Truth identifies three aspects of craving, one of them being craving for non-being.

How does the desire for cessation, to attain final Nibbāna, never to be reborn, differ from the desire for non-existence?
Vibhava tanha (craving not-to-be) is a type of craving. 

Cessation of being (bhava nirodha) is the cessation of craving (tanha nirodha). 

The "desire for cessation" called 'chanda iddhipada' is not a type of craving (tanha). 

Also, bhava nirodha is not "never to be reborn". "Bhava" is "egoism". "Bhava nirodha" is the cessation of egoism. 

If mind believes believes in "ego" or "self", now can it ever stop being "reborn"? 

"Jati" ("birth") itself means "egoism'. "Jati nirodha" happens when egoism stops. 

The only way to reach Nibbana is stopping egoism.