Sarter will not de-energize

Somehow, the battery voltage is getting by the relay switch & to the starter.

Some starters have a drive engagement mechanism that employs another relay.

Could it be a bad ignition switch (the one the key goes into).

Possible. I has a Jet Ski that had a similar problem. A rust short was bridging the starter relay & main battery power solder points. A few minutes with a wire brush fixed that.

Replacing an ignition switch requires disassembling the steering column & pulling the lock cylinder then the switch comes out. An electrical diagram would prove very helpful & most if not all decent automobile service manuals have them & a few even have them in full color detailing each wire color that was installed during manufacture but such diagrams are rare.

But if it is the ignition switch, you should be able to see a voltage with a volt meter on the starter. The ignition switch closes a switch, which sends a voltage signal to the starter that causes the solenoid to to engage the starter. So you should be able to determine if this the ignition switch is open or closed pretty easily.

Jeff