The proper pursuit of Intelligent Laws should seek evidence of an intelligence, not a deity. There would be the simple question of determining whether the laws derived out of chaos or from an aware intelligence.
The only problem is identifying whether or not a law is naturally derived or intelligently derived. What are the defining characteristics of each?
Science should be utilized to establish a chronology for laws of nature/science. In other words, how old are the laws?
An interesting question for knowledge's sake, but I don't understand how this will help identify natural vs. intelligent. Are really, really old laws intelligent, or natural? Are young laws intelligent, or natural? Why?
Are laws front-end fact or do laws evolve with a changing universe?
Again, interesting for knowledge's sake... but how does it help distinguish natural vs. intelligent? Are constant-laws natural or intelligent? Are evolving-laws natural or intelligent? Why?
Science should take these questions as far as they can be taken with observation and statistical inference.
I could be mistaken as I do not work in such fields... but I believe science is already monitoring such things for any detectable variance... for the sake of just knowing what happened and what is.
This is an opening thought.
And it's very good. Best ideas I've heard for identifying intelligence or not. It just needs some specifics and to be fluffed out a bit more. If you can get to the bottom of the two big "why" questions above... you'll be miles ahead of any other intelligence discovery mission.
If there is an intelligence behind things, the laws of the universe should reflect some sort of conscious effort towards a goal... some sort of caring for something. Possibly (but not necessarily) humans or life as a whole. Possibly some aspect of the universe we haven't even discovered yet.
However, if the laws of the universe reflect an unfeeling, unrelenting, unguided march to nothing... it would seem to me that this would lean towards being evidence that they are natural and were not created by an intelligence.