It sounds like the PO tried to install an intermittent wiper gizmo or some suck. Luckily for us, I believe the Europa shares a wiper motor with Spitfires and some (all?) MGs of the time.
The box you show is definitely not a stock part. I’d chuck it.
I think after you take the console cover off and the radio out, you could probably do what needs to be done. You can take the dash out as a last resort. Taking the dash off requires taking out the screws you mentioned, the bottom of the dash is bolted to the top of the backbone (several grounds live there), the steering column bolts to a mount bolted at the bottom of the dash (IIRC). On either end of the dash, there is a bracket that is bolted to the side of the body and the dash. You’ll also have to take care of the heater/demister controls. Like I said, that should be a last resort.
I’d advise you to try to keep up with the Lucas wiring standard and if that is not possible, at least keep up with the green, white, black, brown part of it, but seeing the cars you have, you were probably way ahead of me on that!