Burnt Wire

To avoid causing additional damage while investigating.
Disconnect the battery positive.
Set the multimeter to measure resistance or continuity.
Connect the meter probes (clamps) with one on the battery circuit.
Then start checking for shorts to ground.
First touch the second probe to the first. Thats what a short will look like. If set to resistance it will show close to zero.
Seperate them and thats what it should show when there is no short.
Next touch the second probe to the body, the steering column, the engine block.

If that all passes.
Then turn the key to run and do it again.
You can recheck the accessory and run circuits too. They should have no resistance.

Finally have someone hold the key in start and check for shorts to ground.
You can also check the connections from the battery line to the S1 (yellow) and the Ign 2 (brown). They should be zero.
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Another way to safely look for why the ammeter is showing a high discharge is to install a lamp in the circuit.
The lamp will reduce the current flowing to a few amps. it will also light up whenever a connection is made.
67Dart273 has posted good descriptions of how to do this. If you're interested do a search for his posts how to do it.