The calculation of People Cost in the Short(er) Schedule of Cost Components is less distinct than the 'full' schedule, which provides reasonable definition of what is an 'allowable' cost component.
I don't see any reason why you would not calculate the People cost any differently under the SSCC, however, so a vehicle would be included as part of the rate calculation, where provided by the Contractor.
You would effectively 'liquidate' the cost and proportion this into a daily or hourly rate.
The 'people overhead' is to cover the items listed in the 'Charges' section, which typically includes for 'general Site running costs', so would exclude cars.
As a side issue, you could even review this cost specifically for each project, depending upon the distance travelled and the conditions encountered, to calculate a more accurate 'wear and tear' and 'maintenance' cost' by project, rather than applying an overall 'average'. Not sure Finance / Accounts people will appreciate my comments though !!