Yes, it does sound electrical, but it may be something simple. Does this only happen when you turn the key to the start position and release it? Or does it engage as soon as you reattach the battery?
On the starter motor, there will be a red wire that has power at all times. There will also be a purple wire that only gets power when the key is in that start position. If in some way the purple wire is touching the red wire, the starter will engage.
On the other hand, the starter relay may be faulty.
Let's try something simple. If you open the hood and then the fuse box, you will see the starter relay (see pic 1 below). Switch it with a different relay having the same part number. See if that changes how the starter motor works. Have a helper turn the key for you. If the starter stays engaged with the different relay, pull the relay and see if it stops. If it doesn't, disconnect the battery.
Let me know what you find or if you have other questions.
See pic below.
Image (Click to make bigger)
Sunday, August 28th, 2022 AT 8:54 PM