Handling mileage reimbursement when using actual expenses method

Say as an independent contractor, I choose the actual expenses method for my mixed personal-business use vehicle. Then, maybe next year (I am now locked into the actual expenses method), one client reimburses my mileage at the standard IRS mileage rate. Do these reimbursed miles still count as business miles in determining the % of business use of the vehicle (thus affecting my actual expenses deduction)? And is the reimbursement now taxable (regular income)?  I cannot find an answer in Publication 463 or Form 4562 instructions. Thanks.