Depends. If you own the vehicle personally, then if you have an agreement with the partnership or s corp, you would enter expenses you reimburse yourself from the business as vehicle expenses. in Business.
If you do not have an agreement, then when you enter the K-1 on your personal return. not the home office section, you will be asked do you have to pay any expenses. You will say yes and then enter your vehicle expenses or the standard mileage.
If the partnership or S-corp owns the vehicle, then you would enter it as an asset in Business.