Burnt Wire

Great!
We could sketch the flow like this.
upload_2021-2-28_16-38-2.png

But we don't know which wire yet.

Since you have a portable test light, might be able to narrow it down without taking apart the bulkhead connector.

With the key off, connect the portable test lamp between the battery positive and S2. Then try J3.
If it lights up, then thats the wire to investigate.
upload_2021-2-28_16-47-50.png
If it doesn't light up on either, then maybe its the switch

If it does light up, if you want to double check that its between the bulkhead and the steering column, remove the bulkhead connector. Put the probe into the matching cavity for whichever one turned on the lamp. Then you'll know.

If you've never taken off one of those bulkhead connectors, there's several posts here on FABO about how to do that. A search should turn them up pretty easily.