I think we need to isolate the problem between the solenoid and the Pre-Starting relay R2. Here's the thing - when you push the start button, the first thing that happens is that R2 energizes and closes its contact. That energizes the starter solenoid, closing its contact and connecting the starter motor to the battery. If the contact in R2 sticks closed, the starter solenoid will stay energized and the starter motor will just continue to run. When you turned off the key last night, that killed the ignition, but the bike still stays partially powered up for awhile. The R2 contact, if it is stuck closed, can still supply power to the starter solenoid until Main Relay 1 drops out 40 minutes later.
So, now that the battery has been disconnected all night, leave the key off and only reconnect the battery. If the starter motor stays off, the solenoid isn't stuck. Go remove the covers from the front fuse box and identify R2, then turn on the key. If the starter motor immediately starts to run, yank out R2. If it stops running, get a new R2. If it keeps running, then yes, see if you have voltage to the two small wires on the solenoid with R2 removed. It's coming from someplace else that it shouldn't. Maybe some harness damage someplace.
The other possibility is that overnight, things corrected themselves and you can't repeat the problem. Next time it occurs then, do the R2 test.