1994 Saab 900s oil light question

I recently bought a 1994 Saab 900s. It's a '94 w/ about 135K miles. when we looked at it and test drove it there was not any signs of oil issues. I bought the car and put it on the road; after driving it for about 45 miles or so the oil light came on and it started ticking. I checked the oil, level was good but needed a change (which we knew when we bought it) We changed the oil and added lucas oil treatment. Still oil light coming on ususally after car was driven for a while. Some times it came on sooner though. We removed the oil switch? (at the bottom front of block with black wire running from it to top of engine). It was all gummed up and black with burnt looking oil. We did not have a replacement so we cleaned it up and replaced it. Afterwards we did not have any issues with the oil light coming on for about 3 days (LOTS of driving). Now the past two days it is coming on right when I start it. It is pretty cold here in NY - about 10-15 degrees. Once the car warms up it goes out. Any suggestions??? Thanks