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Do you have an adapter on the tow vehicle that converts the signal from individual brake and turn signals to one signal? That may be the isssue or it may be needing replacement. That can be tested at the converter which is usually up underneath the rear bumper area.
If the taillight converter is bad you won't. Small black box about the size of a pack of cigs. Wires going in and coming out. The brake lead is usually red.
If the stop and turn signals are separate on the vehicle, then there has to be a converter UNLESS they left it off. Not the first time I would have seen that. Easy enough to add one.