It is told in Pin Function Description of datasheet -
Convert Start. Holds the two analog input signals and starts the conversion on the rising edge. Two pulses with SCK in fixed high or fixed low state starts Nap mode. Four or more pulses with SCK in fixed high or fixed low state starts Sleep mode.
But lower on Timing diagram (page 10), you turn LTC1407 to sleep and nap mode without SCK driven. Only CONV pulses, without SCK causes sleep/nap mode.
So what's advised method to initiate nap/sleep mode?