All good suggestions. I would also replace all of the bulbs on that circuit. They can develop internal damage that can short or use extra current.Check the bulbs and sockets.
Check your wiring at the plugs to make sure they aren't frayed and shorting to ground.
Blown fuses indicate the Battery positive current is shorting to ground somewhere in the circuit the fuse feeds or the circuit is being overloaded beyond the rating of the fuse. With a higher amp fuse installed, you need to look for a short.