[Mike_U]

Edit - check out my later post

FRF, thanks for the detailed info and pictures. You are correct. A 6V battery should not charge at 13 Volts.

When you take off the negative battery cable with the tractor and all lights turned off, do you get a spark? If so, that would indicate current is still flowing out of the battery slowly discharging it.

With the tractor shut off for an hour or more until it is completely cool, trace the wires and feel all electrical components. If something is warm, it is likely pulling current from the battery.

There are ways to isolate short circuits and battery draining but in the meantime, auto parts stores and on line sources carry a quick disconnect that you connect to the battery and battery cable and by twisting a knob, you can quickly disconnect the battery from the electrical system without unbolting a battery cable. That should stop the discharging until you find the root cause.

 

[Mike_U]

Heads up. - I looked closer at your photo. You have your multimeter on the Volts AC scale and not the Volts DC scale. The ~ symbol indicates Alternating Current like in your house circuits. Move the selector over to the left hand side Volts scale.

 

[Mike_U]

I had to Google the model no of the silver box on your generator to see what it was.

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It is a cut off box to disconnect the battery from the generator. Here is the website description:
"This is generator cut out only and not a generator regulator. As cut outs they serve only to disconnect the battery from the generator when the generator is stopped or at low RPM. They do not regulate either voltage or current."
I assume if this box is working correctly and wired correctly, your battery should not be discharging back to the generator when the engine is off.

Check out the specs on your generator to make sure it is the correct one for your tractor. Also look for the inputs and outputs of the voltage regulator and measure the voltage going in and out if possible.
I have worked on 6V systems before but have not worked on a John Deere B but if the generator and voltage regulator are working properly, I don't think there should be an AC, (Alternating Current) component at your 6 V battery terminals.

Let us know what the DC battery voltage is after the engine has been stopped a while (or overnight) and then start the tractor and measure the DC voltage of the battery again. If it is the same voltage or less, I'd say your battery is not charging.

 

[Mike_U]

Good work.
I’d say you have two things at play. From the photos, that positive cable looks to be corroded internally so maybe both cables need to be replaced or the connections at both ends of both cables are not as clean as you think. Even with tight connections, if the copper cable or the connectors are corroded, the cable won’t carry high current. Think of it like a plugged water pipe. Nothing can flow out.
Second. The lower voltage with engine running tells me the battery is most likely not being charged by the generator. Find your voltage regulator and check it.

 

[Mike_U]

Yup. Tommyhawk, I agree. Great pics.

FRF, I see the voltage is going up. A bad connection may be your only problem. Seeing sparks at the battery is an indication of a bad cable connection. New cable ends or new cables if needed will solve that. Did you scrape the battery terminals and the inside of the terminals before you bolted them back on the battery? Or the corrosion could on the wire inside the battery cable clamp.

Think of a spark plug gap or a welding rod gap. A spark jumps across a gap but won’t jump if there is no gap. Your terminals have a “gap” at the battery.

 

[Mike_U]

https://www.napaonline.com/en/p/NW_785116?impressionRank=1

Here's a type of quick disconnect switch you can connect to the negative battery terminal and cable if you want a quick way of isolating the battery from the system when the tractor is shut off. It's a lot simpler than removing the cable every time.

While you are shopping, purchase a tube or packet of dielectric grease and coat the new battery terminals and the clean and shiny battery posts when you reassemble everything. It will keep corrosion at bay.

 

[Mike_U]

Wire gauge is dependent on the number of amps that the starter and loads draw from the battery. Too small of a wire gauge and the wire will get hot. In extreme cases, for example if someone tried to use a wire normally used to power lights to power a starter, it will overheat and melt. That's why battery cables are large and have many strands of wire.
If your current wires appear to be sized correctly and are of suitable length, take one of your current wires with you and purchase a similar gauge cable. If in doubt, go to a larger size diameter cable, (lower gauge number). The price difference might be reasonable.

Is the black thing on the cable a female bullet type connector? It is hard to see in the photo.