This was a tricky one to write.
Some people may not have an innate burning desire to track their time. Let me suggest, if it's at all possible to do so politely, that you ought to be curious how you spend your time. Not because you suspect there are ways to optimize it (but there are), and not just because your time is valuable (although it is). But because right now, assuming you don't time track, you simply have no way to make any statements at all about your time.
"But I don't waste time on things!"; "But I'm already too busy!"; "I just want to spend relax more". It's hard for me to properly comprehend why these mean you must be even more careless with your time. And yet those are essentially the clusters of typical responses. Some other people insist how they spend their time doesn't matter that much – and, while there are some value-of-information calculations to do for the truly apathetic, I'd be astonished if that statement made traction in their minds. Unless you are a zen master who has given up all desire, you probably don't like sitting silently in a dark room, or having days of work destroyed suddenly, or being humiliated, or breaking promises to people you care about. How you spend your time matters for those things. It matters for everything you can causally interact with – it must, because you interact with things by spending time on them.
I know people who plan so poorly they will spend most of their time working on things they discard, or on approaches they abandon, while simultaneously spending no time at all on planning. This is particularly frustrating in professional contexts where, even if you're getting paid, it can push you to the limit of your patience. Take notes. Notice you can take time to think through things before you do them. Make sure to take the time to do that for all tasks longer than, let's say, 15 minutes. If you're working with someone else, it's literally your job.
Tracking your time also has a strange effect: it creates a very weak incentive for focused work. At least, if you change tasks 200 times a day it becomes a complete pain to log all of that. And I think focused work may be more valuable as it becomes more challenging in modern workplaces. Email responsiveness is a whole other strange can of etiquette worms I'm going to have to break into later, though: it's just worth pointing out that time tracking isn't utterly transparent – it is a more than just a lens, even when the costs are ludicrously small.
Now that I've dealt with the formalities – making the case for tracking time and acknowledging its biggest weakness – I'd like to say, I care about you. I care how your life goes. I'm not saying I should see your time-tracking records – I definitely should not! – but you should have them. The complete, honest, shame-free picture of what's going on. And then you should look it over, maybe once a week to begin with and less frequently later. It really is important stuff, and I care about you enough to recommend it strongly. Guide your life. Carve out time for the important stuff, sure. But also carve out time for silly things. Have a budget for goofs. Dedicate time to making your life quieter. Or add in planning to make the next thing less frustrating. Or add in time to learn a skill better, so you aren't embarrassed. Do anything you want – but understand the choices you make.