Thanks for the comments and thoughts! The random hour brought about by apostolakisl was something that I had played with as it was simple, but putting a random time within constraints, like between sunset and 2330 same day.
I can see that a couple programs linked might be the answer. Once I get my random day start and get a random time between my parameters.
... and yes, once a week for a random day then my time.
You guys have given me some direction and I will play with it!
John