I myself would recommed to him to mark where we last found blood and come back in the morning to track. Rain or not, if the deer is not hit well, you will more than likely push him further. Let him lay and expire. Also in the daylight, you will have a better chance of spotting him laying in some brush or by a fallen tree where you may in the dark have walked right on by him at 30 or 40 yds or even as little as 20.
Also waiting til the next morning allows the two of you to sit down and recall the hunt to give a better thought as to where the buck may have ran off to, what kind of hit you are possibly looking at, etc.