My wife has a 96 Honda Accord LX Sedan. Starting this morning her right turn signal stays on constantly flashing. Replaced the flasher relay, no fix. Take the switch out of the column and disconnect it, no fix. The left turn signal works normal, but the right stays on at the same time. I can take the flasher out so I dont have flashing signals or annoying clicking all the time and just hope I dont get pulled over for not signaling... Any ideas? Thanks.
It might be the control module in the right front bumper area which has water damage. Have a look at this
HondaWiring-------------
Prepare your future. It wasn't the lack of stones that killed the stone age.
Got it fixed, thanks for the diagram.
Sorry... Well to start with, I feel like an idiot. Never checked the hazard switch in the beginning since only one side was flashing. The switch was bad and not releasing all the way so the contacts on one side were barely touching while the other side was seperated properly. Took apart the switch to take out the contact tabs, bent one a little and it works fine now.
Little note: Dont trust the part numbers if you go to autozone for a new flasher relay. Dont go for the "extra loud" flasher they say to get since its a dollar cheaper. It doesnt even have 3 prongs, only two. Plus its huge and round instead of the block one out of the car. The normal replacement isnt exactly right, but it fits and the clip locks so its good enough. And no I didnt learn the hard way...
Glad you got it fixed. I'm even happier to see that troubleshooters still exist - the kind that understand logic and have the ability to understand "what if" scenarios.
Your problem is similar to what I faced one time where the customer said that her signals didn't work after we installed a remote starter in a Sunfire. Turns out that the hazard switch was in between two positions. 
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Prepare your future. It wasn't the lack of stones that killed the stone age.