I'm willing to OK the first line, "if you break me, I’ll not stop working", even though there has been the occasional case where even the treating doctor judged a death by heart failure to be the consequence of the patient having had his heart broken.
Usually, that will
not happen, so.
A heart that you can touch is likely not to work anymore, but that's not what the wording "my work is
done" implies. It's a phrase that I would use when the guy dies
of old age, or maybe when the heart reached
its own maximum lifetime (cardiac defect), not for the cases where someone rips the chest open and physically interferes with the heart's ability to continue the work it's been set to do.
But it's the third line that's the worst, because you need to change only a single word to make it correct: When you lost your heart to someone, you'll
WANT to "find your (sweet)heart with a ring (= married to you) soon after" - but "must"? I'ld say that those who've fallen head over heels in love are particularly
likely to continue the relationship but
skip on usual rites, material symbols like a ring, even the very act of a formal marriage, if circumstances make obtaining those a problem. And if it's only yourself who has fallen in love but the other doesn't reciprocate, as you suggest, the other's free will even more clearly trumps your "must".
To die when someone rips your heart out of your chest,
that is a "must".
... and, needless to say, these flawed wordings irk me partly
because Mr. King is one of the people I'd expect to wield language with more exactitude ...
