So we know that Johnny is a personality construct that obviously operates separately from V’s brain, as he can have his own opinions about stuff that are different from V’s.
Being a construct, he also doesn’t need to sleep or anything as he cannot feel tired unless he’s in control of V’s body.
The brain is active during sleep, which means that Johnny’s construct is also active and operational during this time.
What do we think Johnny’s thinking while V is asleep, when V hasn’t taken the Johnny-takeover-pills?