Perfectionistic tendencies may be a sign of developing a fixed mindset rather than a growth mindset. One aspect or application is that gifted kids may stop taking appropriate risks in order to always be "right" or always be "smart" or never be "wrong", and this may work against them. The concept is nicely summarized in these youtube videos:
Ashley Merryman & Po Bronson: The Myth of Praise (link-
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Teaching a Growth Mindset (link-
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Parents may wish to read the book Mindset by Carol Dweck for tips on promoting a growth mindset. It is based on years of research. Not that I agree with every idea/application, but on balance found a number of ideas to be useful.