Ok, this is annoying. Got the starter for the Brat a few weeks ago and two days ago it acts up. Dad said it sounds like a solenoid issue and said to see if it can be replaced. Looked at the local part stores and I don't think I can.

 

He told me how he had used a remote solenoid on his 36' Chevy. Can this be done with a gear reduction starter?

If the solenoid is making a loud click and nothing happens then the solenoid contacts are most likely bad inside it. You should be able to purchase new contacts and replace them. Be sure you have made sure that the battery connections are ok by cleaning then. They can cause the same thing to happen also.