Question on basis calculations

The basis of a gift of property for the receiver  (the donee) of the gift is whatever the basis of the giver (the donor) was. Same for holding period (long-term vs. short-term.) However, if the property was under water at the time of the gift (i.e., the fair-market value (FMV) of the gift at time of gift was less than the donor's basis), then the basis for a sale at a loss is the FMV at gift time.

See I.R.C. 1015(a) - https://www.law.cornell.edu/uscode/text/26/1015

But do note that unless the vehicle is used for a business, no loss is allowed upon sale of personal use property and no deduction is allowed that involves basis. Personal-use vehicles are rarely sold at a gain, though yours  may be an exception (if its an antique or you restored it or something).