Water ought not to be much of an issue during this hike, given that I'll be following rivers for much of the way (even the Saejae portion of the path follows some creeks at certain points).
On a recent six-hour hike, I brought along my CamelBak ripoff, which holds a bit more than three liters of water. By the time I got back to my apartment, I had used about half of that amount, which makes sense: I used to bring along three 500-cc bottles of spring water, and they'd all be gone by the end of a long walk. So I consume roughly 1.5 liters of water every six hours. With a 3-plus-liter water bladder on my backpack, I ought to have no trouble at all with hikes up to twelve hours long (I hope there won't be any such hikes!).
But there's another issue to consider: where to re-water, and how? I'll be solving the "how" problem by carrying two empty plastic jugs: one a bit more than two liters in size, the other a bit under two liters. Wherever I can, and using a length of cord when I must, I'll dip the jugs into whatever available watercourse there is; I'll filter the water through a few layers of cloth to strain out most of the grit; I'll drop in my purification tablets to kill off the microbeasties (I also have another set of tablets whose sole purpose is to remove the nasty flavor of the purification tabs), after which I'll run the treated water through my Grayl and pour it into my CamelBak ripoff. That promises to be a long process, taking the better part of an hour, so I hope I'll be doing this only when I'm at the end of a hike, not in the middle of one. If I find myself without stored water but near a watercourse, and I'm thirsty to the point of dying, I'll simply use the Grayl to scoop water straight out of the watercourse. But I don't think things will ever get that dire.
As for the "where": what's the water situation really like? I've gone over my course, leg by leg, and looked at what fraction of each leg will be close to water. Using a three-point rating system, I will now give you an idea of how good or bad the water situation is going to be during the walk. A "3" means "water available most or all of the way along this leg." A "2" means "water available only part of the way." A "1" means "no water available."
Ready? Let's go. (Keep in mind that the trail segments you see below are the unrevised legs: I haven't yet had the chance to comb through everything and redo the legs. That post is coming, I promise. Remain calm.)
Day 1, Leg 1 (camp) = 3
Day 2/Leg 2 (inn) = 3
Day 3/Leg 3 (inn) = 3
Day 4/Leg 4 (inn) = 3
Day 5/Leg 5 (camp) = 3
Day 6/Leg 6 (inn) = 3
Day 7/Leg 7 (inn) = 2 (if I follow a road and not the bike trail)
Day 8/Leg 8 (camp) = 1 (gonna suck)
Day 9/Leg 9 (minbak) = 2 (water @ last half)
Day 10/Leg 10 (camp @ campground) = 3 (leaving Saejae for Nakdonggang path)
Day 11/Leg 11 (hotel) = 3
Day 12/Leg 12 (camp) = 3
Days 13-14/Leg 13 (inn) = 3
Day 15/Leg 14 (camp, maybe hotel in town [Daegu]) = 3
Day 16/Leg 15 (inn) = 3
Day 17/Leg 16 (camp) = 3? (some parts seem set away from water)
Days 18-19/Leg 17 (camp & camp again) = 3
Days 20-21/Leg 18 (hotel) = 3
Day 22/Leg 19 (Toyoko Busan Station #1 Hotel! woo-hoo!) = 3 (but it won't matter*)
UPSHOT: as you see, it's only part of the Saejae trail that's going to be a real problem.** If things are looking bad on Day 8, when I'll be camping and away from any water source, I'll be sure to fill up my two plastic jugs as well as my CamelBak ripoff before I set out on the trail that day. Day 8 is really the only day when water might become an issue. That's not so horrible: I've walked without water in the high desert of Oregon. Not something I'd recommend you try, but walking in such conditions is survivable. Of course, it's stupid to find yourself without water; that can only happen as a result of poor planning. But that's why I'm keeping a record of my planning here, for all to see. There won't be any danger.
*I bet I could hike this segment without water.
**The Saejae trail has another major problem, and I have to thank a Korean-language guidebook for warning me about this: this is the segment where the bike trail merges with regular roads the most often, which makes this the most dangerous part to walk along. The more I learn about the Saejae portion of my walk, the less I like it.