Ignition key position changes the temperature indicated on the warning light and the oil warning light comes on

Hi guys.
I have a question about strange situation with water temperature and warning pressare oil light.
When I turn on the engine of my 19j and I change a little bit position of the ignition key the water temperature showed change. I have mesuread temperature of water inside of the water pump is correct on 68 C on the outsider from radiator tube is 34C, then the water pump and radiator work correctly.
Another difference with a little bit movement of the ignition key is the turn on of the oil pressure warning light.
Anybody has an similar experience?
Thank you for any answer.
Enex

Surely it's normal to have oil pressure warning until the engine is started.