The glow plug light can be very misleading in these cars....If you check the voltage on the glow plugs you will find that voltage is still on the plugs after the light goes out and I wait about 15 seconds of total glow time before cranking ...longer if it is very cold outside...I did not see a year model in the post... I am assuming you have the parallel glow system...The voltage remains on the plugs up to a minute before the relay cuts off the voltage/current to the plugs....It also cuts off when you turn key to (crank) position......
The glow light can be too unreliable at telling you when to crank or not...It is controlled by a temperature sensor ....a timer circuit and a current sense circuit and it gets whacky after time ....I put in a seperate voltmeter gauge to let me know when voltage is present on the plugs before cranking.....This light drove me nuts trying to sort it out...I finally took my relay apart to see what was happening.....
Another thing to check is that the solder pads inside the relay may get cracks in them and should be re-soldered....this is a common failure....
The light ends up doing whatever it does because of the multiple circuit inputs to it changing over time....but generally the relay itself passes voltage to plugs like it should.....whatever the light is doing...If the current path is intact....Just count the seconds before cranking to find your best glow time for your car....There are a lot of posts on this subject so you have plenty of reading material....

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1978 Yellow 300D (The Mustard Toad)
1980 Blue 240D (The Iron Toad)
1989 Grey Mitsu.4WD Mighty Max Pickup (Needs a Diesel transplant bad)

(Open the pod bay doors HAL)