Chiefs!

My humble ride is a Corolla 95 XL, bigbody with 2E engine. My concern is that during mornings, after I start the engine, it would take 30 seconds (sometime more) before the oil lamp shuts-off, and along with the oil light indicator, a "thuck-thuck" sound can be heard. Once the oil indicator shuts-off, the sound also lessens or disappears. With my previous cars, once your start the engine, it would only take about 2 to 3 seconds then the light shuts-off. My worry is that maybe something is wrong with my lubrication system which might affect the whole engine. Can you please help me of what can be the possible causes to the pump abnormalities?

Thank you very much for the suggestions and replies. More Power!