Hi Paul,
I've been working rotating shifts for over 25 years now - that's a lot of nights!!
To begin with. I'd look at how you sleep during the day. Personally, after a night shift, I get through the door and go straight to bed. I find if I stay up beyond 9am I have difficulty getting to sleep. Sleeping patterns are affected by changes in body temperature and just as it is difficult for most people to sleep at night within an hour of running, you may find this for you if you run before getting to bed in the morning.
For me, the ideal is to run within a couple of hours of getting up in the afternoon. Most of the year it is still daylight and I'm fresh and rested. Some days I can't do so due to childcare issues. If this is the case I tend to run before starting work and shower and change at work.
As has been previously stated, experiment and see what works best for you.