Bike rack lights dont work when towing TOAD

The jeep has a separate module to run the trailer electric from the lighting module for the jeep lighting. You need to run a separate wire from the your coach to a second trailer connector on the back of the jeep. DO NOT connect the trailer plug on the jeep to the wiring for the tail lights on the jeep. You will scramble the jeep modules if you tie them together.

Run a separate line to the bike rack.

Pretty normal configuration is the toad lights are fed from the motorhome with diodes in the toad's light wiring to prevent the coach backfeeding the toad wiring system. In such a case your toad trailer conector won't be energized by the motorhome.

If Jeep has diodes in taillights to prevent back-feeding into it's system, the trailer connector is not getting fed.

Based on what you're saying it seems that the jeep side of the plug for the class C is not feeding the same wires as the Jeep itself if that makes sense. How is the Class C wired to the Jeep? Is there a box on the Jeep that the class C feeds into?

Once at the Jeep are there separate wires from the class C all the way back to the taillights? Or are the Class C wires terminated under the dash by the brake pedal?

Another thought. Maybe your Class C is miswired and is actually feeding the Jeep taillights and not the Jeep brake lights. Take a Jeep taillight lens off and check that the same filament lights when you have brakes on the class C and Jeep and bike rack alone.