Cool! Pulsing in a relay/solenoid circuit is usually a weak/high resistance connection In the circuit. A weak connection will pass full voltage until the load draws current. Then the restriction/ resistance will cause the voltage to drop(like a kink in a hose). Because of the way coils draw and employ current with a slight delay, a weak connection can set up a timing loop that causes the coil to pulse.
i dont have access to schematics right now to point you thru the circuit, but if you have a volt meter you can determine if the coil of the solenoid is the issue or if it is something in the circuit.
disconnect and Measure the voltage at the solenoid coil wires and determine which terminal is receiving the +24 and which is ground. You have +24 and ground available Right at the starter so you can use a jumper wire to power the solenoid directly. If it doesnt pulse with power jumped to it directly, solenoid is ok, circuit is suspect. This of course is assuming you are getting 25.0V or greater from the batteries…
Troubleshooting the circuit involves checking voltage along the path to determine where
It is loosing voltage when under load. If I recall correctly the solenoid circuit also powers the heater in the primary filter water separator bowl.