I am going to assume that when you turn the turn signals on, nothing happens, no lights come on outside and no indicators come on in the dash. In other words, they are completely dead.
If this is the case the first thing to do is turn the hazard switch on and off about 30 times as fast as you can.
What can happen is the contacts in the hazard switch for the turn signals sits closed 99.9% of the time. The contacts tend to oxidize. When the contacts are opened and closed there is a very slight rubbing action. This helps keep them clean and making good connection.
I have seen this fix switch problems many times over the years, so give it a try. It fixed my 500SEL when the turn signals quit sometimes. A free fix is always a good thing. A free fix that doesn't help doesn't cost anything. Nothing ventured, nothing gained.

PaulM

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84 500 SEL (307,xxx miles)