What are the fundamental properties of the Universe? If you don't study phenomenon with an open mind, then you may very well misunderstand fundamental properties.
"To which particular deity do you refer, and why should that one specific deity be included in science to the exclusion of all others?"
I don't say that a particular deity should be included. ID is not about which diety. ID is simply about looking at the evidence and concluding that the prevalent scientific explanation is a really poor fit at explaining the observable facts and that an influence (whether outside or inside) other than random mutations and copying errors must be responsible for the design of living creatures.
When we turn up science for which influence is real and which is not, then at that point which diety becomes science. I do, in fact, beleive that their is evidence that points to which diety. And that should be a scientific field of it's own, say the field of Diestic Science. But you aren't ready for that yet.
"Please provide a means to test for this evidence."
If you can't capture an influence/diety in a lab, then you study the way in interacts with observable evidence. If life forms appear suddenly in the fossil record without precursors that appears to be evidence of an intelligent influence of some sort beyond what science has defined as evolutionary factors.
To the extent that an influence/diety results interacts in ways other than creation of life form, study those interactions with the same scientific vigor that you would study anything else.
Two common interactions other than creation of life forms that are ascribed to one particular diety are eyewitness accounts of demonstrations of phenomenal power (miracles) and foreknowledge of human events (prophecy).
We know that there are recorded eyewitness events of demonstrations of phenomenal power (miracles). To the extent that these demonstrations can be studied, study them. A motor vehicle is going to look like a miracle to a first century man. Instantaneous healing of a man's ear also looks like a miracle, but maybe it's using technology we just don't have or understand yet.
Science should never exclude data points or observations that it can't explain. If it did, Science would never advance. Science only advances by developing explanations for data points that it previously couldn't explain.
"God did it" is not an adequate scientific explanation. But "This didn't just happen, something caused this, what?" and "What methods have been employed" and "How was this created" "How does this creation work" are all valid scientific questions.
It shouldn't dote on them, either. It should generally just smile and nod, and move on to problems it can solve.
If it did, Science would never advance.
Science does just fine by constraining itself to looking at data it can do something with. Like predict things, for an apropos example. Unrepeatable miracles, especially those presumed to have happened millions of years ago, are not data points that generally fall into that bin.