I have a 1998 Toyota Tacoma 5 speed and the starter is stuck on , it stays on even after turning key off. I have disconnected battery cable. what do I need to do to fix this problem ?

My daughter's '93 Chevy Suburban has developed several weird symptoms. The windshield wipers come on by themselves and can also be activated by turning on the heater fan or turn signals. My husband tried to find the problem today and ended up removing an added security device (not original equipment) and trailer brake lights wiring. While sitting in the driveway with the ignition switch on (but engine off), we could turn on the wipers with their switch, turn the switch to off position, turn on the left then right turn signals and the wipers would turn off. The gauges would move when we did this, which hubby said was wrong. And each time we turned on something, the radio would turn off and then turn back on. I drove the outfit and the wipers stayed on the whole time, except for a short while when I was stopped. When I would slow down to turn, the "check gauges" light would come on. What would be the easiest thing (and cheapest) to start with in looking for the problem? My daughter has been pulling the fuse but with summer ending and rain starting, this won't be a good option. My husband thought the problem might be a ground wire but there are a mass of wires and he couldn't tell what was what. Relay switch also crossed his mind but he didn't thing that would cause all the other weird activity. Any help would be greatly appreciated!