Like all other Japanese-language Tamagotchis, the Tamagotchi-iD doesn't have a specific Pause feature.
As ShAwDy_1 mentioned, in place of pause, you can use the sleep trick (time-shifting the clock forward to bedtime.)
All toddlers go to bed at 8 PM
Good teens go to bed at 8 PM; bad teens at 9 PM
Adults go to bed at 8 PM, 9 PM, or 10 PM, depending on the character.
All characters wake up at 7 AM.