It should always be on when key is in position 2, engine stopped. Mine takes about 1 second to go out after the engine starts from cold, almost immediately at warm start.
A poor / faulty / pattern filter can cause a longer delay .
When I changed my oil filter for one made by Boshi that came free with my motor it used to take 2-3 seconds for the oil light to go out.
I lived with it for a couple of days and changed the oil filter for a Mahle and the light went out in under a second. Clearly the valve in the filter was faulty
There are a lot of cheap oil filters on the market that compromise on things such as drain back valve quality etc a chap in the USA has done his own tests.
Hi Ivan
The 3ltr Patrol engine is known to have oil pressure sensor problems, it has two f them. There are a number of earlier threads on the subject, it might be worth a search.
Rgds CL