My glow plug indicator will glow red after about 15 seconds or so and stay glowing red until I release the key. If you have a heavy duty amp meter you could put it in series - that would tell you if something has opened in the circuit when your indicator stops glowing. If not that, then if you can test for continuity across the indicator before it cools, it may be that its opening up as it heats. From your description, it would sound like you have a heat sensitive 'open circuit'. Good luck finding the faulty location!
What is the ambient temperature you're trying to start the tractor in? An alternative I have used when I was having glow plug problems a couple winters back was to carefully blow warm air into the air intake hose (past the air filter closer to the engine) with a heat gun on low. Of course be very, very careful to not get the intake hose too hot. The tractor would start without the glow plugs doing this. The temperature was in the 20s when I used this method.
