Oil pressure light stays on after starting

The light is activated by an an oil pressure switch. With the engine not running there is no pressure so it lights up. When the oil recirculates, the pressure increase and the light goes out. Locate yours and change it, they are fairly inexpensive. If it stays lit after a change it may indicate something more serious.

coil, stator, or wire to ground and to kill switch, it is grounding out somewhere - remove from coil to test.that.
Get inline spark tester at princess auto cheapie 6.00 can, or 10 for a good one. spark plug, timing, head gasket burn valve, hard to tell without compression test. if low put cap of oil in cylinder and if goes up is rings, if stays low (under 50lbs should be 90.) if stays low is a valve or head-gasket.
Check plug if dry when trying to start vehicle with choke on then remove spark plug and inspect it.
is carb or fuel problem if dry, is electrical if wet!
check fuses, and stuff and wires but probably a CDI unit to control the spark, or if old is a set of points and condensor and the spark must be triggered by a CDI, a lobe, or a coil CDI unit combo.
The coils on stator send 12 volt, coil to sparkplug send 20,000 volt and the gap in points or ruluctors should be set properly, typically stator to reluctor is set by a book of matches not folded but put piece carboard in between,spark plug gap say double that..
I suspect without more input fuel or spark. if the engine wont turn over the fuel to oil mixture wasnt enough, or the oil injector for fuel mixture if two stroke maybe clogged and may destroy your engine.
I don't suspect this but giving things to consider later.
Some bikes there is wires in a rubber plug as a chaijn indicator and the chain can break this connection, not sure about 4x4 though.
:)

The oil light is supposed to come on when there is low oil pressure, so when the car starts, the pressure goes from 0 to whatever (25-60psi depending on the engine). As a result, the light stays on for a few seconds at the beginning of the start cycle and is then supposed to go out. If the low oil pressure light remains on, then you either have low oil pressure or you have a sensor problem. If you have low oil pressure, you may need a new oil filter. If the filter was just replaced, then you need to get professional help because low oil pressure will wreck your engine in a hurry. Your engine's oil pump may be faulty and need to be replaced.

its an electrical part that when warm malfunctions. id start with coil.

Check fuel pressure, oil pressure switch, AC output from stator, check rotor and diodes

Check the oil pressure switch, and oil level first. Then check rotor brushes and rotor slip rings may need polishing. If the problem is still there check stator and rotor windings

This engine has variable valve timing that uses oil pressure. have had to replace several engines to fix the problem. Try changing oil and using a little thicker oil. example 10w40 instead of 10w30

You say your oil light came on and your engine started "to make more noise". You engine is equipped with hydraulic tappets. If you lost oil pressure, the tappets would have sounded like rocks in a tin can. If you think you have an oil pressure problem, you can check the oil pressure with a gauge. Just in front of the cam chest, there is an oil pressure sending unit. You can unscrew this unit and screw in an oil pressure gauge. Start the engine and see how much pressure you're running. You must use a high quality gauge to test the pressure and you must know how much pressure the engine is supposed to have. I'm sorry but I don't have any specs for the Twin Cam engines. But, if you don't have any oil pressure, your tappets will let you know. They will be noticably loud. Check the wire on the pressure switch and you may want to replace the pressure sending unit.

Good Luck
Steve

that light usually indicates low or no oil pressure, or a broken oil presssure sensor

either you have a bad sensor or you need to put new gaskets on. since its a 1994 it probably needs new gaskets anyways. so that's were i would start. if that doesn't solve it then my bet is its a sensor. but the gaskets should set you back to much. Probably at the most a $100 or so. but a sensor could cost around $250 or more.