Wiper acting stupid

So I guess we have to ask a bunch of questions... Did you recently buy the car in this condition?
Did you remove the instrument panel? Is this when the wiper problem started?
The wiper switch does need to be grounded. If its just dangling from the harness connector that might the problem. I drove my 67 a few weeks without inst' panel. I forget if the wipers would not run or would not stop but I did need to make a little bracket from a piece of plumbers strap to temporarily mount and ground that switch. I did the same for the headlight switch although that switch didn't need a ground.
When inst' panel is removed there are only one or two harness connectors ( depends on model ) and two large wires one red one black involved. Those two wires should be bolted together. I can only imagine someone has placed a cycling circuit breaker here between these two wires. Anyway.. Removing the inst' panel shouldn't result in a lot of loose wires.
The instrument panel was only grounded through its mounting hardware ( which grounded the headlight switch mounted in it, again depending on model ).
A 66 wouldn't have or need the ground jumper at the steering column mount since the slotted blocks in the column mounting bracket were metal. Later blocks were plastic so a little ground jumper was needed. Could you provide pics and more details?