pomester, Thanks for your response and suggestions.......Yes I have been active on this post the Lady with the problem is in Texas and I'm located near Toronto Ontario. I am familiar with the TEAs built in the UK and like you say, you use the gear shift and slot S to start the tractor.
Now this Lady has taken over using this tractor from another family member who is not available to assist. So she tells me that the tag under the steering wheel has TO-85196 Harry Ferguson, I believe it is probably a TO-30, built in or near Detroit Mi. She also offers that the last couple months they have had to charge the battery the day before they needed the tractor, which tells me its not charging the battery. I will also add that her tractor has the " S" gear selector position, but she is not aware of using the gear shift to start it. She tells me that she , checks the tractor is in Neutral, with the bucket down, turns the key, just like a car and the tractor starts up........Now recently her procedure was not working and some one told her to get a new battery, which she did, but after she replaced it , it does nothing I'm lead to believe from what she says.
Her first post was not on this site and because I'm not familiar with the TO-30, I asked to post this on YT. (As this tractor has the gear shift S position I believe it should be very similar to my TEAs i had, but by the picture she has supplied, I think the first place to start would be with some new wiring with proper crimp on spade lugs.
Now , you mentioned it appears to be a 12 Volt system, I thought the battery appeared to be a 6 volt and the operator manual calls out a 6 V, positive (+) ground. Now I am thinking maybe she pulled a wire off while changing the battery other than the main battery post wires, but by looking at her pictures some of those wires if not all of them should be replaced.
My TEAs had a fuse holder on the back of the ignition switch but I think for lights only?? have you seen behind the das of a TO-30??
I have also asked the Lady tonight to get a picture showing the top of the battery and record where the + and - cables are connected to..
I'm goin to let you digest this update, thks for your reply Alex