What does a faint sun line mean in palmistry?

Short answer: A faint sun line usually means the Apollo or recognition theme is present but weak, private or still developing. It does not mean no success.

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Read my palm
A close view of the middle of a palm, with the three long creases easy to see

What this means

First confirm it is a real vertical line toward the ring finger, not skin texture, photo shadow or a temporary crease.

A faint line can point to subtle creative satisfaction, inconsistent visibility or recognition that grows slowly rather than loudly.

Read it with the fate line, head line, Apollo mount and both hands before making any strong claim about fame or achievement.