Intermittent starter issue on DD-60

Just running this past the group for any thoughts...

On my 99 KW with a Series 60 engine, at times and very random, I will turn the key to START and nothing.
No click, no sound..zip. Does this HOT or COLD.

If I back off and turn it again, it will usually then turn over and very quickly.

Here is what I have done so far:
1. Replaced all batteries.
2. Replaced all cables to batteries.
3. Cleaned connections inside stair area.
4. Cleaned all connections on Delco Starter.
5. Cleaned all connections on Delco piggyback solenoid.
6. Replaced ignition switch and cleaned all connections.
7. Made sure everything is tight and sprayed with anti-corrosive.

...not sure what else to look at. If I heard a click and nothing, then I might suspect the starter perhaps.

Does anyone know if there is an additional solenoid after the ignition switch, perhaps on the firewall or ?
- thats the only thing I can think of before up and replacing the Delco starter and piggyback solenoid.

PS. Someone also mentioned there might be an upgrade to this starter. Smaller, lighter and with a reduction gear.

If anyone knows about that, it could be helpful if/when I opt to replace the starter.

 

And then THIS relay connects to the starter piggyback solenoid?

...if so, that could be the culprit....

 

According to KW, it's located in the battery box area and about $56.

 

HA! - yea...that was a fun time back then...