Typical wiring for wipers on Grady's are as follows;
Orange - park, (unswitched) hot all the time.
Orange/green stripe - port wiper, (switched).
Orange/black or white stripe - Starboard wiper, (switched).
Black - (ground), motor frame.
Even if the colors are different, the important thing is, the striped wires, (switched) control the wipers.
The solid orange wire feeds full time power to the motors, allowing them to park, after being switched off.
The wiper motor should be marked with - "park", "1" and "2", (1 and 2 are fast and slow speeds). Ground is usually the frame.
The "orange and ?" striped wire you mention, should not be disconnected. Both of the striped wires should be connected to the bottom of the dash switch. One lugg for each striped wire. The switch must be a dpst, (double pole, single throw). The 2 luggs should be side by side.
Are you the original owner?... if not, my guess is the previous owner either had a problem with the wipers, (park) and altered the wiring. Or... they added the second, (port) wiper and couldn't get the park feature to work and again... altered the wiring. That's where the double pole switch comes in. It has 2 circuits. If someone added the second wiper and simply connected the 2 striped wires together, (say... on a single pole switch) the park feature will not work. The wipers will continue to run, (after switching off) due to feed back, untill both hit their park point at the same exact time. that can sometimes be a very long time, lol.
First thing you need to do is, check the wiring on both the motors and the dash switch. Once you have the wiring right... if there's a problem, you may have to disconnect and run one wiper motor at a time to find it.
Even if you have a single pole switch, there is a way around it, but first, check out your wiring.
Hope this hepled, if not... pm me and we'll take it from there.