I cannot comment on the specific nature of the 350, however, every time that light has done things that are not expected on mine, one or more than one of the glow plugs are not working properly.

I believe that the first thing you need to do is to check each glow plug with a sensitive ohmmeter and verify that the readings are below 1 ohm on all of them. If you find any that are above 1 ohm, or open, change them.

If this fails to resolve the problem, then the relay might be the culprit.