The duration the glowplug light is on dependant on engine temp. Now, even though the light goes out and you have started the engine, they are still on for up to about 1 min, again based on temp.
Checking the GPs is real easy. Get a basic meter, place the pos. lead on the GP it'self or, even easier, pull the GP connection off at the GP relay. There are 5 "sockets" in this connector. Place the positive lead in one and the neg. lead on a good ground, the battery is best. Good plugs should read no more than .5 ohms. Anything more and the glowplugs are on their way out. Obviously an open means the wire inside the GP tip has broken all together. The resistence gets higher as the GPs wear, until it becomes an open. GPs are very much like light bulbs, there is a "wire" inside that touches the metal tip, and like a light bulb, when it "burns out" like a light bulb's filament, it creates an open and no longer works. You could touch each GP tip to check resistence, but thery are harder to get at than using the connector in the GP relay.

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1999 MB SL500 (110,000 mi)
2004 Volvo V70 2.5T (220,000 mi)
2014 Tesla Model S 85 (136,000 mi)
MBCA member