Hello and thank you for your question.
Unless the trailer has an engine that burns fuel, you probably won't be allocating fuel to the trailer. The gas is used in the truck, which may or may not be hauling a trailer (for business purposes).
Vehicles are listed property and it is important to keep track of their business use percentage for purposes of depreciation. See IRC 280F, here:
There is no deduction for personal expenses (IRC 262) with respect to a trailer or automobile generally (ie... save for taxes perhaps, IRC 164), so for either, you should be keeping track of your personal use percentage and allocating the deductibility of your expenses accordingly.
I trust this answers your question. Thank you again!