I've got a similar situation I am trying to find. Brand new battery, battery has a full charge. 3 out of four times everything starts just fine with engine "firing" immediately. 1 out of 4 times I can hear a click that sounds like the starter relay but nothing happens. Then I immediately do another glow plug cycle and the engine starts just fine.

The PO did mention the problem before purchase and he suspected the starter relay but had never spent any time tracking down the problem as it would start on the second try. The problem appears to be more prevelent if I try the starter immediately after the glow plug light goes off but the problem is random enough that I am not sure whether this is a good correlation. The relay looks fairly new, though.

One hypothesis that I have not yet tested is that the GP relay is sticking. Assuming that the light is trigged by the input side of the relay, not the output, the light would go out but the GPs would still be pulling enough current to not allow the starter to engage. This would also explain that supposedly the problem does not occur when I wait longer after the GP light turns off.

Since I can hear the "click" of the supposed starter relay I am assuming that both it is good and that the ignition swith is good but if the GP test turns up nothing I'll test those items next.

I'll post my results on this thread.

Edit: PS battery connections cleaned and ground connection cleaned.