By the sounds of the shot you describe, I would have to say it sounds like a gut shot. Every deer I have ever hit through the lungs has took off like their tail was on fire and their ass was catchin. That's not to say that every deer ever shot in the world will do the same though. ALso what makes me think this is the fact he stopped and stood for a while while swishing his tail. Not too long ago, about 2 weeks ago, I took a shot at a nice mature doe. Just as he triger on my release tripped, she lunged at another doe and I caught her just behind he last rib in the gut. She only ran about 30 yards and stood there looking around and wiggled her tail a few times then walked off. I heard her go down, but not hard, kinda like she bedded a little harder than normal. It was early so I just stayed in my stand. I gave her an hour and then I heard her rolling and a bunch of gurggling. I eased out of my stand and headed back to my truck for a drink and a fresh chew. After a couple hours I figured she was dead. I headed back into my stand site and took up the trail. It was still broad daylight so I nocked another arrow and started to ease in, hoping to find her dead or too stiff to get up and put another one in her. When I got to the spot i last seen her she jumpped up and took off. I watched her go another 40 yards and then she turned and went aboutanother 20 yrds and I heard a crash and then silence. I backed out and waited until after dark and came back with my hunting partner and my brother and we found her dead where I last heard her crash. I think you did the best possible thing by letting him go over night. If the shot was a little back and you never pushed him you should find him within 150 yards. I find most deer will stay on a main run until they die or just before they die they will leave the trail. Also a lot of times a deer will head back the way they came as they know they were safe up to this point. Good luck on your recovery.

LIVE TO HUNT,HUNT TO LIVE.