My biggest buck to date we found the next day. I was a young kid probably 15 years old and shot him with a .243. Hit him a little back and was able to get another shot off as he was running off. Gave him about an hour before I got out of stand to look for him. Went to where he was first shot and found blood. Started tracking about 100 yards into following blood trail I jumped him. I back off for another hour. After the second hour I started the search again. Lost trail after about 50 yards. It was pitch black at this point and my brother and father had now joined the search. We searched for hours into he night. Never found him. Went back the next morning and found him within 30 minutes. He had made a huge circle and doubled back towards the stand after I jumped him. I actually him second shot as well as the first. Needless to say my motto is to look until you find them.

This makes me curious in case I'm ever in the situation: what is the natural reaction for a deer that's been shot that runs into the woods? Is it to head down a trail as indicated above? Is it headed for lower areas, higher ground, good safe bedding area, etc? Just curious what their natural instincts would lead them to do. Or is it totally random because they're in panic mode since they've just been shot.....and they have no logic at all.....

found the problem

Lots of opinions on this one. One of the indicators often mentioned is whether or not the deer ran with its tail up. While it’s been thrown around for decades that a hit deer will run with its tail down, research has shown it has no bearing at all. A deer that has been hit is just as likely to run with its tail up as it would with its tail down.

One of the things I have seen through my own experience is that a deer that has been hit just behind the shoulder (heart and lung shot) will kick the front legs backward just as it might if hit in this area with a fist. A gut shot deer will often hunch up as you might when hit in the stomach. And sometimes a well hit deer will show no sign at all that it just took a bullet.

An old timer that I hunted with for many years said that a deer that has been hit will seldom if ever be seen jumping during its exit. I have found this to be true myself. A deer that runs away with stiff front legs was likely hit solid.

And lastly, it’s long since been said that a hit deer will run to water. Lots of theories on why this could be true. Never seen any research to prove it either way. Some have explained it as deer preferring to run down hill, which can often lead them to a stream or creek they are unable to cross before expiring.

Years ago, I shot a doe with a very accurate 6.5 X 55 Swedish Mauser. Range was under 100 yards and I hit her 6 times, the 6th shot broke her spine. My young son, in the blind with me, witnessed the sorry performance/result. Made me sick, I have never since seen a deer with that amount of vitality.
Thankfully, every deer killed since that day was a one shot kill, some with a short tracking job and many with instant kills.
I still have nightmares about the riddled doe.
I gifted my son-in-law with the Mauser.