Has the contactor worked correctly in the past for you?
The engine RPM won't change until there is a load applied.
Without a load it's supposed to run at 3,050 RPM.
At full load the RPM would be 3,450 RPM.
I'd suggest making the following DC voltage measurements to narrow down the problem.
1) Connect your handheld meters negative lead to chassis ground.
2) With Battle Short
OFF start the generator.
3) Verify that inside the three relays that only the
rightmost one has its internal LED illuminated. Is it?
While
holding the Contactor switch
UP measure the DC voltage at the following points in the following order.
a) S5-5
b) S7-8
c) S7-9
d) K15-8
e) K15-12
f) K12-4
g) K12-12
Post the DC voltages at each of them. They will be either about 0 volts or about 24 volts.
Also answer to question 3.
Here are the terminal layout for the relay sockets. Same layout for K12.
View attachment 883912
-