Yes, if your turn signals in the back use the same filaments as the brakes, the multi-switch must allow the brake signal through when the turn signals are not activated. There are multiple diagrams for your system, so I'm not sure what you have. If you have the light blue wire that goes from the brake switch ul the column to the turn switch, make sure it is getting power when the pedal is pressed. It should go thru the switch as shown in the second diagram below.
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