Yeah, I knew about Mr. Pirsig and I've always loved the book.
Depends how impatient you are - or perhaps more accurately, how your financial situation is. Because of my marketing background, I started off with a large company (CSC Computer Sciences as it was then) working with a team that was launching a large collection of 'service offerings' - so the writing, while it had to be accurate and truthful, focused on upbeat, marketing-style messaging. It took me 5 years - including some time as a freelancer - before I began to get regular gigs in my target zone - you know, bringing complex software to life for a readership that was largely composed of developers.
If I was doing it again ... and to get into that zone a bit quicker ... I would definitely look at the open source world and offer to help with some projects that gave me some tingles. There are many, many wonderful open source projects that owe their success to great docs (e.g. DJango) and in the closed source world, orgs like Stripe are very well regarded.
I always took two sayings to heart:
1. You need to write a million words before you can call yourself a writer - both Ray Bradbury and Jerry Pournelle are cited as sources.
2. All writing is rewriting. That is, your first draft will be garbage but it's easier to improve on something that you have, than to start with a blank page.
Both quotes have been more often attributed to writing fiction, but the same goes in the tech writing world.
The other important thing to understand is that tech writing is much less glamorous than development, and so it's often harder to fill those slots, which gives you an edge if you can demonstrate a bit of ability.
One option you might consider is simply to apply for those jobs. If you know programming, that's a huge plus. If you don't have a portfolio - urge the hiring company to set you a tech writing task (that's what I did). You can only learn from the exercise. Sure, you might bomb a couple of times, but there will come a time when you don't.
You don't really get much from books until you're into the groove - tech writing is really just about 'doing it' while keeping an authentic picture of your reader in your mind.
Hit me up (I'll put my email in my profile) if you have any other questions.
[Edit]: for presentation and a typo