Re: 62 Gale electric start issue
So, the motor will crank if you jump the solenoid. That means the starter and ground are ok. Now you need to find out why the solenoid won't do it. You say you have a 12V circuit tester (a light, I assume?)
There are two small terminals on the solenoid. Check for voltage on each of them as somebody turns the key to the start position. There should be 12V on one and zero on the other, and the solenoid should click. Are those the results you get? If yes, then check the voltages on the the two big solenoid terminals WHILE IT IS CLICKED. You should get nominal battery voltage of about 12V. If you have battery voltage on the battery cable side of the solenoid, but not on the starter side of the solenoid. the solenoid is bad (unlikely). If low or no voltage on the battery side, check your battery and battery connections. Matter of fact, battery connections should have been the FIRST thing you checked. Don't just look at them, take them apart and clean them shiny bright, then reassemble tightly.
OK, back to the solenoid. If it did NOT click, and you have no voltage on either small terminal, check the fuse, wiring, and key switch to see what is preventing electricity from getting to the solenoid when you turn the key. If it did NOT click, and you have voltage on BOTH small terminals, there is a problem with the safety switch or wiring between the solenoid and safety switch. A quick diagnostic test is to ground the safety switch wire. If it cranks, the safety switch is burned up or being held open by the throttle.
This is a condensed version of the tests. Hopefully by now the problem has been located. If not, come back with the exact results you got and we will take it from there.