1) Pick up a new radiator fan switch. They're cheap and the best engine insurance out there. Also, pull the cap off the coolant reservoir (when cold). Start the car up and look into the tank. There should be a steady stream of coolant into the bottle. If not, the return hose could be clogged. There is a restrictor in the line right before the bottle. You can drill it out and completely remove it without any harm to the motor (provided you extract all the pieces.
Also, you can test the functioning of the fans (without the AC), by pulling the plug from the rad fan switch. Jumper the terminals of the RED wire to the RED WIRE WITH WHITE STRIPE. The fan should come on low. Now, jumper the RED wire to the OTHER wire (sometimes red with black stripe, sometimes red with brown stripe). The fans should come on high. If not, check the fuses in the cabin and the relay in the cabin (sometimes mounted to the ran shroud).
2) Nipples: there should only be one open small nipple, and it should connect to the hard plastic hose that is usually WHITE or YELLOW. Block off the other nipple if it's not blocked off. Later ECO diesels used the separate nipple to connect to the air box. This does not apply to your car.
3) Now you know the light works. Now, you just need to figure out why it does not work when you try to start the car. Even on a hot day, the light should come on for a few seconds. Check the relay.
As for staying on, it means you have water in the water separator. Under the car on the passenger side near the rear wheel is a small white (usually yellowed from age) box with a knob on it. Loosen the knob and let the fluid drain out. It should be a mix of water and diesel fuel. You may to actually pump/plunge the knob to get the fluid out (it works like a plunger once it's been unscrewed all the way).
If the light stays on after that, you may consider cutting the wires to the water level sensor. I'm not sure exactly what to do (since I've never done it), but it's a common delete. Be sure to NOT cut the wires to your fuel level sending unit. Use the search function and look for water separator.
Good luck.