I haven't had time to really research this yet, but I hope my brain is scrambled and I'm missing something obvious ...

With the new law eliminating Employee Job Expenses on Schedule A, will it be fully taxable to the employee if a taxpayer uses a company vehicle for business purposes?

The second paragraph sounds like an Accountable Plan ... will that be taxable to the employee?

Publication 15b:

This exclusion applies to property and services you provide to an employee so that the employee can perform his or her job. It applies to the extent the employee could deduct the cost of the property or services as a business expense or depreciation expense if he or she had paid for it. The employee must meet any substantiation requirements that apply to the deduction. Examples of working condition benefits include an employee's use of a company car for business, an employer-provided cell phone provided primarily for noncompensatory business purposes, and job-related education provided to an employee.

This exclusion also applies to a cash payment you provide for an employee's expenses for a specific or prearranged business activity for which a deduction is otherwise allowable to the employee. You must require the employee to verify that the payment is actually used for those expenses and to return any unused part of the payment.

For information on deductible employee business expenses, see Unreimbursed Employee Expenses in Pub. 529.