I own a Suzuki Swift diesel. When I start the car in the morning during first time in the day, the oil pressure light stays on for 4-5 seconds after engine has started. Also when I restart the car when engine is hot, light goes off immediately. Is this normal to have light come on during cold start as oil has all settled down to sump.
It's common for the oil pressure light to stay on longer from a cold start - as you rightly surmise, the oil has all settled down into the sump, and so it needs to build up pressure. Some diesels also use thicker oil than petrol cars, which will take longer to build up pressure (but equally will take longer to drain down).
How old is the car? it might be that the oil pump is starting to get a bit tired and so taking longer to build up pressure. It's also worth making sure you've got a decent filter on it - many cheaper ones don't have an anti-drain-down valve in them, so you also have to fill the filter each time you start from cold, instead of it staying full of oil.