I am having issuses with the taillights. Brake lights work, turn signals work on 2003 Suzuki XL-7

Seems like everything is working but the tail lights...I dont see a fuse in the fuse box marked taillights

Fuse number 36 (10 amp) marked tail is the fuse you are looking for but there is a light switch, relays and a body control module in the circuit. There is a company that independent auto repair shops get their information from, this same information is available inexpensively for people that work on their own cars.. The information is year make and model specific, covering repair procedures, torque specifications, fluid capacities and specifications, service bulletins, component locations, wiring diagrams ect.... Alldata is very easy to navigate
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1 more answer
The tail lights are on a different power feed than the brake lights and turn signals. It is possible that both tail light lamps are burnt our, or you could have some other problem. Try replacing both bulbs and if that doesn't resolve the issue, take it to a shop that does electrical work.