Morning Bondy,
It's always darkest before the dawn. Between us all we'll get this one sorted for you.
I'm not surprised the seat switch has been disarmed and that the magneto kill was not put through the ignition switch.
There are two seperate circuits that have been butchered. One is the start control and power, the other is the magneto cut-off. The magneto cut-off is nice and simple with an earth being provided to turn the ignition off. The replacement engine should have a standard arrangement where the magneto is grounded when the throttle lever is pushed to the max slow position. If this isn't how it's working then perhaps the lever is being stopped by the cable or the lever slot before it gets to the cut off point. This is something you can check out seperate to the wiring issues.
Ultimately we can look at putting the magneto kill through the ignition switch for convenience and sort out the seat switch but for now if you can get it to cut off with the throttle lever with an adjustment then we can concentrate on the start system first.
I'll take some photos and draw you a mud map of what the start system needs to look like. It might seem a bit overwhelming but it's not that complicated. In the meantime if you can draw a mud map of what you have including wire colour, dead ends, etc it could be a tremendous help.
