I have a 1983 g1 yamaha gas golf cart that won't start from the accelerator. .I've already cleaned all on the connections on the battery starter and solenoids. .it will start if I press down on the accelerator and cross out the solenoid. ..

SOURCE: 1981 Corvette will not start

The neutral safety switch is located in the shifter housing.

Here is a link to a good article on this topic, that would beat an explanation from me.

Brian

Yes, it sounds like the NSS is the culprit.

SOURCE: Yamaha xj600 doesn't start

hi m8,, i guess u have a neutral light lit up 2,, u need that to start it as well,, no light and she wont go ,, or try pulling the clutch lever in as u push the starter,, ,if none of that works,, then 1st u can do a quick experiment ,, grab a rubber or plastic handled screw driver, and cross the two terminals on the solonoid, if she turns over then the starter button needs cleaning up, or may have a break in the wire,

SOURCE: solenoid starter problems

sometimes is better to replace the entire starter and not just the solenoid that way they are usually under a lifetime warranty and you can just exchange them. it does sound like you have gotten faulty solenoids though.

SOURCE: 98 yamaha grizzly atv my starter just goes click

take a screw driver and lay it across the solenoid. if the engine cranks the solenoid is bad, if it still dose no turn over either the starter its self is bad, or the battery is junk. have the battery tested before you go buy any other parts.

SOURCE: My 98 golf won t start intermittently. I replaced

If you run a push button directly from the battery to the solenoid, the engine will crank when you push the button.

If the no start condition is because of the solenoid, this will not fix the issue.

If the no start condition is related to circuitry of the ignition system and/or fuel system, this may fix the issue, but may not, as well.