I don't think there are any kinds of jobs that I would reject for someone just because they are introverted. Granted this person may need some alone time to recharge, they can be surprisingly social in some cases. While I can acknowledge the question is kind of fun to ponder, maybe I'll think about this some and have a different answer.
Personality Test links:
A few more answers:
From lifemastertraining.com:
Suggested Job Type Almost any career,
though often attracted to the justice
system, the military, the corporate
world and academia. Questioners often
like being part of a team. Also health
care and education. Quality
Management, Quality Control,
Inspection, etc.
From thegreatofficeescape.com:
Type 6 – I have read a lot about
phobic/counterphobic sixes in various
enneagram books and I must say that
it’s hard to buy into the hype. A
“counterphobic six” is really just a
mood they might go through on a bad
day. And certainly when considering a
career, a six should think about who
they really are, which is friendly,
adaptable, cautious, meticulous, loyal
and a great team player. By nature,
they are not daredevil lawbreakers
and, in the long run, would not be
happy in occupations with high risk,
no matter how “counterphobic” they may
be feeling!
Suggested Careers for Sixes: There are
plenty of great careers for sixes,
providing there are plenty of jobs
available.
* Paralegal
* Elementary School Teacher
* Child-Care Worker
* Administrative Assistant/Secretary
* Credit/Loans Officer or Counselor
* Escort/Security Guard
* Financial Aid Counselor
* Public Notary
* Actuarial Scientist
* Health and Safety Inspector
* Banker
* Technical Support
* Insurance Underwriter
From russellrowe.com:
Careers that appeal to Enneagram type SIXES
Though Sixes can be found in almost any career, they are often attracted to the justice > system, the military, the corporate world, and academia. Truth, justice, security, stability and belonging are big issues for Sixes so naturally they like to go into professions that give them the opportunity to protect others, fight injustices and allow themselves to feel safe, secure and part of a team. Many are in health care and education.
Counterphobic Sixes sometimes have jobs that involve risk. Those who lean toward the antiauthoritarian side are usually happier when self-employed. If Sixes are unhappy with their work situation, they are likely to become rebellious or secretive.