Hi Nat
I LOVE those Lightburn Twinnies. There must have been a wide variety of models as I have seen about a dozen and no two identical. I haven't seen one for over 10 years, though.
The spinner outer tub is galvanized sheetmetal which rusts away - check you don't have any leaks dripping onto the motor or wiring.
There is no seal where the spinner shaft passes through the spinner outer tub. The tub has a raised "collar" in the centre, about 3 or 4 inches high, and the spinner can has a dished base which goes down around the collar at the outside. So the collar fits up under the spin can into the dished section. To not leak, it depends on the spinner pumping out the water faster than water is spun out of the clothes. It is possible to load too much water into the spinner, it overflows over the collar and over the spin motor, though there is a shroud over the motor too. Not really up to modern safety standards...
Another cause of overflowing in the spin can - there is a one-way valve between the spinner and the wash tub, so that if you open the drain valve when the motor isn't operating, you don't drain the wash tub into the spin tub. If the non-return valve (from memory it's a rubber flap inside the pump??) is damaged, then when you open the drain valve and the pump isn't running, water flows from wash tub to pump to spin tub over collar onto motor and floor.
If any of these events have happened, the wiring or motor will be wet, which would trip the safety switch.
Another trouble I had with one of these - the wash tub seals to the top via a rubber seal like a diaphragm - a rubber sheet which fits over the wash tub and has a square hole in it to fit the aperture in the grey fibreglass top panel. The rubber disintegrates over time, the wash paddle is very vigorous and flings water up against the seal with every stroke. If the seal is damaged, water gets up and over the edge of the wash tub.
about 15 years ago I did rust repairs on one of these twinnies, the same as yours except twin motor. The old Scottish lady who owned it was the grandmother of a friend of my partner. She had owned it since new, about 25 years at the time. She bought it on the recommendation of a farmer she knew who ran a sheep staion. they said no other machine coped with serious farm dirt like the Lightburn.
Best of luck with it.
Chris.