What the diagram will show is that when the key is placed in the Start position, the current must pass from the “B” terminal on the key to the “S” terminal on the key, and then through the PTO safety switch (deck must be disengaged), and then through the Neutral Safety Switch (foot must be on the brake), before the starter solenoid’s coil can be energized, provided the solenoid housing is well grounded. If the tractor were new to me, and I intended to keep it, I would (1) remove the solenoid’s mounting bolts and make sure solenoid was well grounded before replacing the mounting bolts complete with star washers.
I would then proceed to (2) clean the terminals on the Neutral Safety Switch and Ohm it out to make sure it was working well electrically and mechanically.
(3) With the battery installed and connected —but the Neutral Safety Switch disconnected— I would check to see if I had battery voltage on one side of the Neutral Safety Switch. (4) If I had the same voltage at the Neutral Safety Switch as I had at the battery (or nearly so), and I was satisfied the Neutral Safety Switch worked and that the spring steel actuator was present on the brake pedal rod and adjusted correctly, I would re-connect the Neutral Safety Switch, and the motor should turn over with the key.
(5) If I didn’t have good voltage at the Neutral Safety Switch, I would go back to the key, remove and clean (possibly replace) all the terminations, remove and Ohm out the key to see that “B” connected to “I” in the “ON” position, and that “B” connected to both “I” and “S” in the Start position. (Best Ohmmed out from wire end of terminals connected to the key with the battery disconnected.)
(6) Once I was satisfied the key was working, and that the terminations were secure mechanically and electrically, I would re-install the key and check for voltage at the Neutral Safety Switch with the key in the Start position (battery connected); again, if I had good voltage at the Neutral Safety Switch, I would expect the tractor to turn over with the key.
(7) If I still didn’t have good voltage at the Neutral Safety Switch, then I would go to the PTO Safety Switch; again, looking for solid terminations and good voltages and any wiring “anomalies” I might encounter along the way.
Of course, if your Neutral Safety Switch actuator is missing (as mine was when I first acquired my 149) you could easily bypass it temporarily, for diagnostic purposes.
Over the years I have encountered and resolved all the problems I describe above on one or the other of my tractors.
Hope this helps.
PS: If you can’t find either the Neutral Safety Switch or its actuator present on the bottom of your tractor, you may find two wires hanging down in the general vicinity, one of which might have a smidgen of electrical tape on it. Chances are, if you twist the two wires together, your circuit will be complete, at least that was the situation I found on one of my tractors.