In general, if you to need to fix your car with more damaged (may around the car) the insurer will charge you for deductible and of course you have to pay more than 2,000 due to they not calculate per time of accident but they will calculate by total amount for repair even your car is rental car or private car. For example ,if you have claim 30,000 baht (many damages around ) the insurer will charge you 3,000-5,000 based on the consideration of the claim department.
The insurer have to keep deductible in policy of rental car because they need to control if client have claim many time for a small damage. And also control your loss as well because if you have a lot of claim it would affect your premium in the renewal years.