Izuzu Rodeo Starter Problem.No solenoid click.Battery ok.Starter relay swapped.Starter will spin when jumped to battery but does not engage without solenoid action.Might be ignition or neutral switch?
It is a neutral switch.
Starters on newer Isuzu will have a safety-switch installed,
even for manual transmissions. The switch, inside the transmission
or clutch, will disable the starter circuit until the vehicle is in
the proper "mode" to engage the starter.
For automatics, this means the starter won't engage unless the
transmission is in Park or Neutral.
For manuals, (stick-shifts) this means you must engage the
clutch while turning the key. Until you engage the clutch, it
will seem like the starter is dead.
You can have a look at the related link for some trouble
The safety-switch(called a Mode switch for AT) is on the side of
the transmission and the clutch switch is on a bracket in front of
the clutch pedal. It is activated (switches on) once the clutch
pedal is depressed.