You are correct that the sentence:
The new pair of scissors I have purchased are blunt.
is grammatically correct. You are also correct that it is an elision, or shortening of
The new pair of scissors that I have purchased are blunt.
The general principle is that modern English permits such elision whenever the result is clear and not ambiguous. Long ago English grammar was stricter. I think this is partly due to the great amount of borrowing that has been done to increase the vocabulary of English. Grammar from other languages often came with that vocabulary, and so many exceptions to rules became common, until the rules themselves were looser, I think.
("There is no point in arguing over what is or is not legitimate English. English is the result of attempts by Norman men-at-arms to make dates with Saxon barmaids, and no more legitimate than any of the other results." - The Other Human Race by H. Beam Piper)
Beyond the general principle that elision, particularly of relative pronouns, is allowed when the meaning is clear, the only rule that I k now of is custom, or what people are not used to, particularly fluent speakers. I am sorry that that isn't very helpful, but it is the best that I can do.