Should I be wearing Invisalign overnight only?

Sounds like a recipe for a poor or delayed result. Think about it. You move them while sleeping, then they drift during the day, then, you move them while sleeping and they drift again the following day.  If this doesn't create problems, at a minimum it will take much longer to move them than if you were to just wear them as close to 24 hours a day as possible.

I have all my patients wearing 24 hours. You might want to ask you orthodontist if your treatment would progress quicker if you wore it for the 24 hour period.

I am not sure why you would be told to just wear Invisalign aligners at night if you want to move your teeth.  Wearing them part time will not likely result in adequate tooth movement.  Invisalign recommends 22 hours per day, and I do too.  You may be able to wear them a little less often than 22 hours a day and have your teeth move, but the less time you wear them throughout the day, the less effective they are.  
I do recommend to my patients to wear retainers at least 8 hours a day in order to maintain where their teeth are currently at.