Hello and welcome to JustAnswers,
Sounds like your career is moving along well and growth is being achieved with new and better opportunities. Can understand your concern about a background check if it is something that might conflict with what you wish to be hired for.
A background check will have an overview of where you worked so your job as a consultant may not show up in their system. If your consulting job consists of outside work for this car dealership and not on the direct payroll, it is possible that the consulting work may not show up as if it did the work may just be listed as internet consultant and nothing specific.I would suggest that you might wish to run your own background check on yourself to see what is being reported as to be prepared as well as correct any mistakes on the report. You can do this for free as the following link can provide assistance is ordering this for yourself:
Going into any interview, one needs to be as honest as possible. Unless the consultant job is asked about in the interview, no need to explain it. If though asked, then talk about consulting work you have done without going into detail. Without it on the resume and being a consultant, odds are that the position may not come up on a background check. Only if you were a direct hire and on the payroll for the car dealership that it would show up.
Please let me know of any additional questions/concerns you might have and also if you could take a quick moment to rate my assistance so that I can receive credit for helping you today.
Best in the interview and the new opportunity!
Still not a problem as you might be asked in an interview about the job and what is was about. Never hurts though to list it on a resume as it shows that you were employed and accomplishing productive objectives for the car dealership. I would suggest to run your own background check to make sure first that there are no errors on your report. You should then receive an interview I am sure and only if asked about the consulting job that you can talk about the work and what you offered to the dealership. Does not hurt to explain as well as shows various traits that you can offer the new employer.