Some comments
The situation seems to be the one that I addressed, albeit with a different example.
If the Ascendant is Virgo and the job (10th) is Gemini:
Start by assigning Mercury to the querent:
Then check the tenth for any planet in Gemini and in the tenth, if so use that as the significator of the job.
If there is no planet in Gemini and the tenth, go for a natural ruler of career, profession and social status - the Sun is the obvious one, for any job. If the querent has told you the type of job, then you might choose a bit more selectively - jupiter for any legal profession or for any religious profession, Mars for the armed services or the police or security services or the security industry, Venus for arts, including the performing arts, fashion, entertainment, leisure, would be some examples.
The same principles apply where you have Jupiter ruling both houses, though there things are a little easier as you can use Venus as the exaltation planet in Pisces.
For Aquarius and Capricorn, you have Mars exalted in Capricorn as the exaltation planet.
For Taurus and Libra you have Moon in Taurus and Saturn in Libra, so there's always a deputy standing by
For Scorpio and Aries you have the Sun exalted in Aries.
However in all cases check to see if there's a suitable planet in the house, before choosing the exaltation planet and even then, if an obvious natural significator is available, it's always worth considering.
As you get more experienced you might find situations in which you find it 'fits' better to use a different significator for the querent but don't do that till your confident about your methodology.
There are some questions that are solely about the querent in themselves or in regard to their homes. In these questions the Ascendant ruler signifies both the querent and the quesited. In that case follow Barleywine's suggestion about judging on the basis of the condition of the Lord of the Ascendant.
I'd only use the sixth for a job, if I was the employer or manager of the person doing it - for example if I was an employer considering the merits of a potential employee or asking the question 'Will the plumber turn up to mend my leaking tap?' - the plumber is my 'servant' for this particular task and I'm his/her 'employer' if only for a brief time.
On using the seventh for a date:
'Will Q have a date with B?' is a seventh house issue as it involves two separate people who are not connected in any other way. 'Will Q go on a date with his/her friend B?' moves the question to the eleventh because B's current relationship with Q is not just any two people or even two named but unrelated people.
Sometimes you have to think a bit to know what the querent is really asking
'Will I get a date next month?' could be a question asked by someone who just wants to go on a date no strings attached to get out of the house, or who would like to go on a date for a good night out and some fun. In such cases I would use the fifth house, the question really is about the activity and about having a good time.
If the same question is asked by someone and you feel that they are really looking for more than a date - they see it as hopefully being the start of a long term romance, then the question shifts to the seventh - it's the relationship of two people that has become important, not having a good night out. How do you know which it is - you ask the querent, as nicely as possible, what his/her hopes are, plus you get a feeling from talking to them what they are really looking for.