Well, you are applying for a job, be it part time or full time and therefore this letter should fall into the formal category. So, this is how you should end a formal letter;Your faithfully,
( you need to sign with the full name there as it is important for the employer)
I am writing to apply for this great job, tour guide, and to see if it is possible for you to provide me with more details regarding to this job.
Here too, you better refer to the source that you found about this job vacancy in the first sentence of your letter.