The travel to pick up the car in your locality ("Tax home") is non deductible commuting. The cost to get to an "out of town" location is deductible. So, in your example, the 5 mile pick up is not deductible, but the 1000 miles is. The IRS has no fixed mileage rule for what is out of town. Out of town is outside your metropolitan area.
So, yes you do qualify for #2.
