You are learning about "fusible links." A fusible link looks like a wire but there is much more to its design. The wire is small so it melts when overloaded. The insulation over the melting wire is designed to stand the temp and remains in place so the ends of the burnt wire are not shorting out.
This is one example of a fusible link.
More info at this link:
What Is a Fusible Link and How Do You Repair One in Your Car?
You cannot replace a fusible link with a piece of ordinary wire. You can find fusible link wire on line but it comes in different load carrying capacities so selecting the correct one is a bit of a challenge. Better a fusible link too small a gauge than one too big.
New tractors use "Slow Blow" fuses in place of fusible links.
This is a link to a slow blow fuse on ebay.com. Ideally you would have to find the socket the fuse would plug into.
Amazon.com: 3 Pcs 32V 3 A PAL Pacific Cartridge Slow Blow Fuse: Automotive
We need a wiring diagram to better point you in the right direction.
Tractors with any electronics have diodes built into their wiring harness
These diodes are becoming the norm in most farm machinery and garden machinery as more and more electronic components are being used.
When a starter relay or solenoid is energized, a strong magnetic field builds up around the small wire winding's. These are the winding's which power the relay or solenoid.
When you release the key from start, the magnetic field collapses suddenly and in doing so can generate voltage spikes of hundreds of volts.
This phenomenon is called flyback.
Diodes are now used to bleed off the voltage spikes.
Sometimes, when owners are jump starting their tractor, a tiny mis connection of the booster cable polarity blows the diode and now you can have a dead short.
Poor grounds for the starter can cause lots of grief as starter current is flowing backwards up smaller wires.
Add a ground cable with an eye on each end from where the present ground cable attaches to the engine or frame to a starter mounting bolt.
The starter relies on a good ground connection between the engine block and the starter. Rust on these mating surfaces can increase the resistance to current flow.
Dave
M7040