Thanks for the data, Rod. That is an Intek engine, not a side-valve, which I had not known up until now. Here is the Illustrated Parts List:
http://bsintek.basco.com/BriggsDocumentDisplay/18mmwHXDnfBhU7y.pdf

Here is the Operator's Manual:
http://bsintek.basco.com/BriggsDocumentDisplay/msuwEN-K_ny7tH217FzoPu.pdf

Your engine was built on 24 May, 2004.

When you have put your wiring into order and re-checked the machine's operation, we can move forward from there. By the way, putting some types of tenant's improvements right can be fairly difficult. I remember, without nostalgia, one case we had where an auto elec had installed a bridge rectifier in place of a single diode and apparently felt badly about having two left-over terminals on the bridge, so he connected them to two unrelated circuits. The resulting diagnostic outcomes were weird to say the least. Here is the thread:
https://www.outdoorking-forum.com.au/forum/ubbthreads.php?ubb=showflat&Number=34212&page=1