Here is a quote from the service manual for your generator. (in the files section of this forum)
Fault Shutdown Sequence
"Check Engine" Faults: The following fault
switches shut down the genset by grounding terminal
2 on fault breaker CB2, causing it to trip:
. High engine temperature switch S2
. Low coolant level switch S3, via relay K6
. Low oil pressure with S4
. High exhaust temperature switch S5
. AVRo overspeed circuit
Based on this and the schematic contained in the same manual it appears the above noted switches are "normally open" and they close to provide a ground path when they go into a fault condition (i.e. too high of an exhaust temperature). So, the failed terminal would prevent the switch from activating. I can't account for why Bill's genset ran when the broken terminals were connected together as it would appear that would create a permanent fault condition, unless there was another work around by the technicians.
You can test this theory by grounding the broken terminal to the non-broken terminal while the genset is running and seeing if the genset shuts down, or by measuring continuity across the switch as Bill suggested.
By not having the S5 switch functional your system is missing a fairly important safety device and you should replace it at your earliest.
All the best,
Gary S. Silver
Amel SM 2000 #335
Puerto Del Ray Fajardo Puerto Rico