The electrical system in 1988 Jeep Wrangler is very simple. There is not a whole lot to it. If this problem is not caused by a defective turn signal switch, then it is being caused by a bad ground. This is not the type of electrical malfunction that would be caused by a "fuse" or a "relay".
The wiring diagrams for that vehicle show the ground connections, but there is no information in the service manual that tells you where these grounds are located (That is just the way things were back in 1988) You simply have to LOOK for them. The one that is most likely the problem, is the one that grounds the headlamps to the body. If you follow the harness for the headlamps, you will be very likely to find it.
There should be a ground point or two on the fire-wall, then there may be one or two in the engine compartment on the fender aprons. There is likely to be one or two under the dash.
So, you need to check all your ground points and make sure they are clean and tight and not all rusted-up.
To see the "Ground Distribution" diagrams for your Jeep. click HERE
Please note that the file at the link above will be deleted from the file server in a few days due to copyright restrictions.
I highlighted the things you said were malfunctioning. My guess would be that the grounds shown as G305 and G306 are the ones that are messed up. Your wipers are turning on when the components on these grounds are trying to find ground and they are grounding THROUGH your wiper motor circuits.
Also be sure to check the ground straps/cables that connect to the engine block.