If your father requires 24 hour care, that means during the night he would need assistance from a caregiver that would need to be either constantly awake or be woken up when your father needs him. If this is the case, one caregiver should not be allowed to go on both night and daytime duties. It’s not safe since any lack of sleep would diminish his performance the next day and that would not be fair to him and to the patient.
Be wary if a caregiver says he could do it because chances are he is thinking about the money and not his own safety and his patient’s.
There are cases when a caregiver wakes up twice or thrice in the middle of the night to assist a patient to urinate and then go back to sleep. But that is not the same as getting real good sleep and if this goes on and on, in a few weeks, the caregiver would look like a total wreck.
To give good 24 hour care for your father, my opinion is you need two caregivers doing night and day shifts probably interchangeably on a weekly basis. Rates between 10–13 an hour is not unheard of for this position, licensed or unlicensed. Either way it’s going to cost money, hiring from an agency or not. It’s which caregiver that matches your father’s personality and temperament that’s also important to consider. What you want are caregivers that are patient and kind and would form happy relationships with your father.