55.2-59 55.2 Starter question

[55Trucker]

Hi all - I have a 1955.2 3100, 4-speed, 235 L6. For the past few years the starter engages about half the time, and I've finally gotten around to figuring out what's going on. The problem is, when I press the floor starter button the starter gear doesn't seem to engage - I hear a higher pitched whirring sound. Try it again, and the gear engages and the starter cranks and the engine starts.

The starter itself does not have an external solenoid, and before I remove the starter and open it up, I'm hoping someone can point be in the right direction.

Thank you, John