Glow plug light turns off early
 

Own a 1983 300TD. Sometimes the glow plug light turns off too soon and then it is hard to start. It acts like the glow plugs did not turn on--black smoke and a slow start. Recycling the key does not help turn the glow plugs on when this happens. My mechanic says the glow plugs do not need to be replaced and it does start fine when the light cycles through the heat up (amber light on for agout 5 seconds). Any help on this issue would be appreciated.
Thanks

Thanks! will make the change.