When it is hot see if it will Crank OK if you use a jumper wire (use a rag or cotton/leather gloves to hold the wire) across the Terminal Block in front of the Battery. The 2 screws on the Left are connected together already. Jumper from left of the plastic devider to the small screw on the right
If jumping ther terminal block works OK every time you man have an Ingition Switch problem or a Nutral Safety Switch Problem.
You can find out if you give the Starter Solenoid a wack with something made of wood inbetween to see if it jars something in the solenoid.
Always a good idea to check and (safely) clean all the Electrical Connections before discarding the Starter.
The area labled "Contacts" is a area in the Solenoid that can get burned up over time. One member claimed he takes the Solenoid apart and rotates those copper contacts to a fresh spot that is not burned. I have not tried this so I do not know if it is difficult to do or not.