A multi-meter and some leads with aligator clips may be helpful for this and future diagnostics.
Spend some time looking at the wiring diagram - in fact drawing a copy of the circuits of interest is a good way to get familiar with how things work.
You are probably right, but I must ask, how do you know this?
Did you do a spark check with a screw driver or spark tester?
Two possibilities that I can think of.
1. Switch is faulty.
2. Wires shorting allowing the alternator and ignition to get power - possibly direct from the alternator.
For visual checks I would look at
a. The ignition circuits wiring under the hood. This includes the alternator's 'field' wire and the ignition start circuit.
b. Steering column connector and wires.