Hmm.. I'm a 1997-and-newer Ford guy, so I can't help much.
Here's a link to the Winnie wiring diagrams for your coach.
Are both the front and rear turn signals not working? How about at the trailer hitch connector? How do all the turn signals behave with the hazard switch activated?
Do you know the chassis designation for your coach?
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Mark 2008 Holiday Rambler Admiral 30PDD (Ford F-53 chassis) 2009 Honda Fit Sport
Just for fun, put in one new bulb to see if it works.
I don't really expect it to, but you need to eliminate that as a possibility.
Bad ground?
Grab a piece of wire out of your junk drawer (or wherever you keep your spare wire), connect one end to ground somewhere on the frame and tuck the other end between the bulb and the socket - along the side of the bulb (don't let it touch the contacts on the bottom).
If doing that makes that particular bulb work then you've got a bad ground connection somewhere.
I had my brake lights go dark on my '94 Bounder. There's a relay under the hood that had gone bad. Replaced that and all was good. Had to cut back the wires a couple inches and put on new connectors too. Corrosion on that old of a vehicle is a challenge. It affects the grounds as well.
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'02 Winnebago Journey DL, DSDP, 36' of fun.