I of course defer to stronger players, who can study however they damn well please. But if a beginner asked me for advice, I would tell him that "solving" a tsumego doesn't mean finding one line that works, it means going through all the lines that work. If you can't do that, you didn't solve the tsumego. If you do solve it, you got it right. And if you can't solve ~80% of your problems, you should find an easier set.
Although the warning that solving means being able to answer all responses is spot on, I take issue with the rest. For one thing, even pros miss lines and so just believing you got every line right is no proof of anything useful. There is reassurance in looking at a solution.
There are also valuable lessons. Telling a beginner to glare at a problem until he sees light at the end of a tunnel is a good way of reinforcing bad habits. He will probably go "if I play there, he plays there, and then I play there, but if goes there I have to answer there, and then - oh where was I?"
Problems are not solved by such bushy tree searches. Restricting ourselves to weak players (i.e. most of us here), they are best solved by identifying the various key shapes and weak points and then superimposing patterns of known sequences on these. Looking at a solution first can help pinpoint the shapes and catalogue the sequences in your brain. With many (all?) of the patterns there is no mystical osmosis required. You can break down the pattern into easily understood chunks. E.g. the tombstone tesuji has three elements: (1) push through and cut, (2) add sacrifice stones, (3) fill the outside liberties. Once you learn that, you can learn the refinements (e.g. part 1 may not be completely applicable, or in part 3 you need to be careful about the order of filling liberties).
I submit that even a beginner could be taught swiftly to solve tombstone problems by this method, but it would take the fabled army of monkeys with a tripewriter, or a genius, to solve these rather long problems with the stare and glare method.
There are also heuristics that can be applied. E.g. "there is often a good move at the 2-1 point". This is backed by research. Some Japanese guy recently calculated that in problems where such a move was possible, it was the right first move about (I think) 17% of the time, and the right second move 9% of the time. Such heuristics are often contained in the texts of solutions.
As I said in my review of Kyushin Tsumego, there is a large body of pros who are happy to recommend peeking at solutions - with the important caveat that you must look at the problem often, so that the patterns get wired into your brain. Even for those pros who recommend stare and glare, we are entitled to ask if what they say is applicable to us. I suspect that they are really addressing a go population (an Oriental one) where they can assume that at least a decent proportion of the readers have already learnt the basic patterns in the way I described for the tombstone. In terms of the same review, they are advising people who are ready to move onto the applications or combat stage. Since, as far as I know, virtually nothing has been presented in English that enables readers to learn the basics (the kata) as above, such advice to western readers is often irrelevant and even harmful. Although we lack books on the kata, by looking at solutions
and (importantly) the way they are presented, we can deduce many of the kata ourselves. I don't believe stare and glare is an efficient, or even a plausible, way of deducing the kata, because it induces looking at individual moves rather than complete sequences.
Try learning a karate kata, or dance steps by just watching someone else. It's an awful lot easier when you have a teacher who breaks it all up into small units and shouts out: left foot forward, right arm back with hand to the waist, make a fist, twist and punch. That's how tsumego can and should be taught - the punch bit is especially fun
I particularly like the advice, "Don't try to win the review"!
for 
, black has got this move in even if white wins the ko. That's what dictates the timing in this case.
is a tesuji that lets black take the ko first with 
.