Light comes on at start up and shuts off when

I am not familiar with the model so I am not aware of any quirks it might have.

It has to be assumed the oil light is telling the truth and there is in fact little or no oil pressure on initial start up.
An oil switch doesn't put the light on at zero pressure but whenever the pressure falls below whatever the minimum rating of the specified switch happens to be - the lowest I have encountered is 4lb and others have been as high as 12lb sq in.

I have encountered similar problems before and on all occasions except two it was caused by oil drain back - due to time and gravity the oil in the lubrication system would drain back into the oil pan causing a "dry start".
The causes for this have variously been a low oil level, an excessively worn oil pump, a fractured or displaced oil suction pipe or the wrong oil filter. This refers to the canister type or spin-on filter, some of which contained a valve to prevent drain back. The valve wasn't incorporated into the offerings of many aftermarket suppliers.

The other two instances were caused by a partial blockage of the suction pipe gauze filter by the collapse or pushing up of the steel oil pan after being heavily grounded.

Oil light is rather important it goes out if oil pressure is good comes on if oil pressure is low when it comes on damage is expected with continued operation like wearing of main bearings and pistons and cylinders can lead to a engine rebuild

it could be a sticking oil pressure relieve valve when cold or a weak oil pressure switch when cold. the oil pressure should be checked when first started cold.

The oil light comes on when the car shuts off because there is no oil pressure. Make sure it has oil in it. If so take the car and get the codes pulled off the obd computer.

Sounds like the oil pressure sending unit needs replaced.

sounds like you may have a defective oil pressure sending unit.

dies the truck restart once it cools off? it is very common for th 6.0 to have high pressure oil issues on a hot soak. they will run till the cows come home but once shut off they can not build up enough pressure by cranking speed alone to start truck until it cools down and the seals become rigid enough to bridge the gaps they are sealing in the first please. if this is the case. it may be the STC fitting ojn the back of the high pressure oil pump (intake and turbos must be removed to check) or possibly the branch tube o rings have worn. the branch tubes are located under the valve covers and supply the fuel injectors the oil they need to perform their "power stroke"...

Oil light that comes on while in idle means the oil pump screen is clogged or damaged, cause low oil pressure to the engine. That part is only $30. It could be a bad oil pump though, if that is the case the pump can run you $100. Either way you need to get it fixed ASAP it can cause major damage to the engine in a very short period of time!

you might try and change the pcv valve, my car hand a similar problem in the summer and i never changed it. the pressure blew my cam seal and i was leaking oil like crazy. i dont know if it will fix it but they are cheap. i would give it a try.