no, you totally missed the most important part, twice:
**Problem: the windshield wipers come on when the head lights are turned on, and go off when the headlights are turned off**
the intermittent wipers not working 'problem' you have focused on and answered (twice) is _not_ the problem, it is instead intentionally put in the system to allow the car to be driveable--thesequence of actions to try to get the wipers to stay off when the headlights are turned on were:
1. the switch on the steering column was ruled out as the problem by unplugging all leads to the stalk (and the wipers _still_ were on/off with the headlights)
2. all front, rear and side lights grounds were checked, cleaned bright and set tight. (_still_ wipers on/off with lights)
3. headlight switch replaced and several of those easiest to get to grounds under the dash were serviced/checked...(but still wipers on/off with lights)
4. to make it drivable, the intermittent circuit in the N10 relay was disabled. (so your last instruction to get a new working N10 is wrong...i have a working N10, and when not disabled the wipers are on/off with the lights..
5. drove it like that until he had time to fool with it again and when he again enabled the N10 intermittent relay it was *fixed*, like magic with nothing else done..
6. then a few weeks later it started again...i downloaded and studied wiring diagrams and saw a path through the washer reservoir...so i wiggled the electrical connection on the reservoir and it was
7. until last weekend and _again_ wipers come on with lights...
8. mechanic rechecked grounds, ran out of time and again disabled the intermittent wiper circuit in the N10.
this may be hopeless....i know i have already used more of your time than you like . . . but it ain't fixed yet...
if you don't have any advice other than replace the N10 or check grounds i'll move on..
i may just sell it, as is..