I want to improve my perception and reaction time to help me respond to incoming attacks more quickly. What techniques can I use to improve perception and reaction time?
TL;DR the best way for you to improve your perception and reaction time is to train and spar with opponents at a school or club, under the guidance of an experienced coach or instructor.
Seriously, nothing sharpens your perception quite like getting hit.As has been pointed out in the comments, my answer may seem like I'm saying "go out and get hurt". This is absolutely not what I mean! In a class, you will learn to spar and fight in a controlled environment.
Now, I'm not suggesting you go out on the street looking for someone to attack - that way leads to the dark side, padawan! What you really need to do is find a school/club/gym that offers some fight or martial art training; once you've found such a place, join up and start training as often as practical.
Learning to spar and fight in a controlled environment is the key point of my original answer. In taekwondo, we have various different types of sparring that allow us to increase the realism without compromising safety; at the highest level (in class), free sparring, with safety kit, allows us to approximate a real fight (with the stress and adrenaline that goes with it) without serious harm.
At first, you'll get hit a lot. It will be demoralising and painful, but it will start to help. You'll also need to listen to comments, hints and tips from your opponents and coaches/instructors.
Improving your perception and reaction time for fighting is something that can only really be improved by repeatedly sparring with real opponents; I don't know of any drills you can do on your own.
It will take time and it may feel like you're not getting any better, even after several months of training - remember that the people you're training with will also be getting better, making it harder to see your own improvement. Again, listen to your coach and training partners; they will be able to tell you if you're improving.
Finally, Sardathrion commented that you could set a beep to sound at a random interval, hitting a bag when you hear the beep. This is true and will help somewhat, but it is no substitute for actually sparring with someone; it will not help you learn how to read an opponent for an incoming strike and it won't help you experience how you react when you feel threatened or under pressure.
One thing you can do that very directly targets improved reactions is find a partner to practice with, and take turns with one of you trying to deliver fast, untelegraphed strikes - stopping just in front of the defender, or with protective gear to allow contact without injury - while the other side starts from a generic sparring stance and attempts to consistently dodge, deflect or block the attacks. Start with something simple like a jab blocked with the palm of the defenders front hand - defending just needs a twist of the forearm - and eventually increase the number of allowed attacks and targets (e.g. jab, reverse punch, front kick or low kick). If the attackers finds it way too easy, get them to stand back and have to close distance more during the attack. The defender can challenge themself further by trying to deliver a nice counterattack simultaneous with or extremely soon after defending, which the original attacker might or might not try to defend against.
I'm not sure if it's a current concern of yours, but another aspect of perception is peripheral vision - you should find the above can aid development of peripheral awareness once you start mixing techniques like low and high attacks.