No, do not continue to file Schedule C if you had not business activity in 2023. It would seem you had no reason to use your vehicle for business if you had no income in 2023. You can add you vehicle back to your return when and if you have business activity in a future year. Keep in mind that any sale or trade of your vehicle will be a taxable event if you used the standard mileage rate (SMR) or depreciation on your vehicle.
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