will 385.13(a) put my truck out of service
No. Across all roadside inspections in our database, 385.13(a) has never resulted in an out-of-service placement. The OOS rate for this violation is 0.0%, meaning inspectors do not have the authority or practice to immediately ground your vehicle for this citation alone.
However, this is a serious administrative violation that affects your carrier's safety rating. You should address it immediately with your fleet's safety and compliance team.