Looking at VJ's job responsibilities window, it says 'remodelling', 'painting' (if not maxed), 'reviews'. So, no - no other skills appears to pertain to this profession.
The issue with painting not giving job exp might be a bug, since logic-based activities give exp to investigators, and turning in captured spirits gives exp to ghost hunters. It looks like a pattern to me - a main skill, the jobs themselves, and a side activity to provide job exp. I have no idea about the other professions, but maybe we could "investigate" further after this little project?
*hands dark side cookies and hugsies to MrsFlynn just because*