I had a glow plug go out last month and it did the exhact thing your's is doing.
The glow light would not come on but the relay was working. The engine would start, run rough for a little bit, then it would smooth out and the glow light would come on for a few minunits. Replaced the bad plug and it was back to normal. By the way, my car won't start at all if the glow plug relay or fuse is bad. My diesel is a 91 but I am sure they are almost the same.

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84 500 SEL (307,xxx miles)