These little engines are surprisingly robust---they were built to be driven by a nation who have only 2 throttle positions--fully on/fully off! Also when they were originally built, the quality of lubricating oil was nowhere as good as it is today. For the relatively low cost involved I would be tempted to (a) fit a new oil pressure switch (front, right side of engine crank-case), (b) change the engine oil--a good quality 20/50 will be perfectly adequate and, (c) CLEAN OUT THE OIL FILTER! This last job is often neglected--the filter is the aluminium centre of the crank-shaft pulley (where the fan-belt is--6 bolts--10mm spanner--only the filter cover will come off). It is awkward to get the filter cover off with the rear cross-member in place, but easier than taking the whole cross-member off. With the filter cover off, you will see what looks like 'rubber' in it (and the pulley)--this is the centrifuged muck that has been spun out of the engine oil. Make sure the gunge is cleaned completely from both the inside of the crank-pulley and the filter cover and that there are no bits left that could be circulated round the engine. Although the filter cover will only fit back in one position, I would mark the cover and the pulley (dab of tippex or similar) in order that the filter cover goes back in its correct position 1st time of fitting---it has the timing marks on it, so it is VERY important that it goes back in the correct position. I would also make sure that the electrical connection to the oil-pressure switch is good.
With the above work done, start the engine, let it get nice and hot and see if you still have the problem. The oil light will probably come on when the engine is idling (hot), but MUST go off as soon as you rev it.
