I had a feeling you would not want to leave the tractor with the battery connected until this problem is solved. I want to reinforce that statement for the safety of your tractor and barn.
You have an intermittent short that can and very well might cause a fire when you are nowhere near the tractor.
You are close to the solution but not yet close enough to risk a bad outcome.
Since your tractor is a 98 model it could have enough time on one of the battery cables to render it incapable of handling the load of the electrical system when you go to crank the engine, thus all these weird things happening with buzzing relays, turn signal ghosts etc.
I would verify with someone's assistance, ( have them move the ground cable as you seek out voltage drop(s) ), that the ground to chassis from the battery is good with no intermittent issues. Then same with the positive cable. Just to be sure- you have replaced the battery, yes? With a new one of same CCA etc.?
If there is any question of the ground location of the battery ground wire running to the chassis change the ground wire with the same exact gauge wire and crimped on connector on the chassis/frame end, the bolt that connects it to the chassis and any metal that it comes in contact with must be bright and clean of any oxidation, black or burned coloration, etc. Shiny new metal color, then coat with Vaseline or dielectric grease, (or battery terminal anti- corrosion spray AFTER attaching the bolt/washer, etc. to the clean metal). Clean the area with sandpaper and then clean off the sandpaper residue with Brakleen or a similar metal cleaner.
Once the above conditions are met you are ready to troubleshoot other possible avenues of cause/effect. Not until you have verified all this can you effectively solve the problem- and you may get lucky and solve it by doing the above.
Good luck, and DISCONNECT the battery when not in its presence! PLEASE!:2cents: