A loaded reefer burns fuel while it sits, whether the tractor is hooked or not.
The unit runs to hold temperature. A dropped trailer in the yard is not waiting. It is working. Who pays for that time has to be on the rate confirmation before the doors close.
Write the line before you load
Say when the free time ends and what the reefer detention pays after that. Fuel has been expensive this month, so a weekend in the yard is not a small argument to have on Monday.
If the confirmation is silent, you and the carrier will invent two different bills. Write one bill before the load.