You and me both. We must be doing something wrong. :)
I've been working since I was in 9th grade and have NEVER had enough money saved up to take 3 weeks off, much less 13 months.
If you save 6% of your take-home income for one year, you'll have saved enough to take three weeks off. So if you take home, say, $500/week, put $30 each week into a savings account. You won't even notice that it's gone.
If you want to take 13 months off, the best strategy is to move from high ground to low ground. Eg, take a job in a city like SF, Denver, Seattle, NYC, etc that pays well, get a cheap place, get rid of any vehicles and use public trans, etc. Taking home $75k and socking away 1/3rd each week, you'll end up with $25k in savings - which is more than enough to spend 13 months roaming the country.
(In the past few years I've spent > 13 months roaming the country)
What does anyone do in the US who finds themselves unemployed? They scramble to find a job..any job to make ends meet and when that doesn't happen, they live out of their car. And when they lose their car, they live in a homeless shelter.