1982 300TD Fully caharged battery dies after a few cranks

I have a 1982 123, 300TD and noticed the good battery dies quickly after just a few cranks of the engine. I tested each glow plug terminal with a light as shown on the cool videos you have, and noticed that two of the five do not light up. I looked at the glow plug relay fuse and it is OK, could I possibly have a short in those two glow plugs that would cause it to kill the battery that fast? Please help :(

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