Which personality trait(s) characterize high need for external validation? Some background to explain my question:
I recently overheard a conversation, between two men working in the same firm.
One of them (A) is thinking about finding a new job, as he is not happy where he is. The other (B) says "A, you have very valuable skills in this, nobody else knows as much as you do about this! You will have no problem at all finding a better job!"

I can see and hear that A is very hesitant to find a new job, he looks uncertain and not convinced that he will indeed find a better job.
A says he feels a need for external validation. A does not seem to have low self-esteem, so the need for external validation seems to be unrelated to self-esteem. 

In the Big 5, which personality trait(s) would explain such a need for external validation?
Neuroticism and agreeableness might be able to answer the question, but that depends on the following:


Would a high-neuroticism low-agreeableness person crave for external validation?
Is high agreeableness alone enough to make someone crave for external validation?
Is high neuroticism alone enough to make someone crave for external validation?
The Big Five model (OCEAN) of personality is based on statistical analysis of a person's tendency to agree or disagree with short descriptive statements, and consists of the following component dimensions:


Openness to experience (O): general appreciation for art, emotion, adventure, unusual ideas, imagination, curiosity, and variety of experience.
Conscientiousness (C): tendency to show self-discipline, act dutifully, and aim for achievement against measures or outside expectations.
Extraversion (E): breadth of activities (as opposed to depth), surgency from external activity/situations, and energy creation from external means.
Agreeableness (A): general concern for social harmony and importance placed on getting along with others.
Neuroticism (N): tendency to experience negative emotions, such as anger, anxiety, or depression.


Of these, I would argue that the trait which most directly maps on to the concept of a "need for validation" by itself would be Agreeableness. This is the short answer.

We can, however, imagine a person who is high on Agreeableness, but for personal/cultural/religious reasons does not directly value others' approval; we can similarly imagine a person who is high on Neuroticism and experiences social anxiety, seeking others' approval to alleviate that anxiety. This can be extended to any combination of traits. These more indirect means of obtaining "need for validation" behaviors means that it is difficult to speak confidently of any one set of Big Five traits, and only that set of traits, mapping on to "need for validation."