Starter system troubleshooting, possible culprit found

This morning, I used the start system troubleshooting procedures in the service manual (that thing is essential!). The first test requires jumping the contacts in the starter relay. I had disconnected the ground terminal on the battery before jumping the relay, and as I was reconnecting it, the starter began cranking! This was confusing to me, as I hadn't put the key in the ignition yet. Before the battery could die, I tapped the jumper, and the starter stopped. Hopping in the cab, I attempted to start it properly. It started without issue. Not wanting to die of CO poisoning (I was in a closed garage). I pensively shut the engine back off, and completely removed the jumper, checked the ground terminal again, opened the garage door, and attempted to start the engine again. No cranking this time. My hypothesis is that the relay contacts are shot, and they still intermittently conduct, but they are finally working less of the time rather than more. I'm heading to Autozone to pick up a new relay, hopefully it works.