I don't think he is that well-developed, and to me at least, he is a hateful man. Galad and Elayne have their weaknesses and strengths, but the only thing I see of Gawyn's personality is being good with sharp, pointy things.

Perhaps his character arc was for him to accept his predestined position as a tool?

The Urban Dictionary has a definition of the slang term, 'tool', that interestingly enough encapsulates Gawyns' personality and hilariously enough, sketches out certain scenes that happened to him during his POVs in ToM! Read on: "A person, typically male, who says or does things that cause you to give them a 'what-are-you-even-doing-here' look. The 'what-are-you-even-doing-here' look is classified by a glare in the tool's direction and is usually accompanied by muttering of how big of a tool they are. The tool is usually someone who is unwelcome but no one has the balls to tell them to get lost. The tool is alwasys making comments that are out-of-place, out-of-line or just plain stupid. The tool is always trying too hard to fit in, and because of this, never will. However, the tool is useful because you can use them for things; money, rides, ect."