I wish I was a step expert, but I am not, so I can’t say if the override switch not working is the reason for the ignition “on” putting stairs out when normally it brings them in (under certain conditions) for safety reasons. I think the override switch places 12vdc onto the controller (basic Kwikee step wiring diagram attached) so perhaps the fuse for that switch has blown; or switch is bad ? Not sure where that fuse is located though, but you can use a voltmeter to test for 12vdc on the override switch contacts or white wire on the controller (switch would apply 12v or remove it depending on position if the switch is working). I am also not certain if that fuse is blown, if that would also cause the ignition issue too. If there are no “step experts out there” might be wise to call the manufacturer and see if they can advise based on your two known symptoms. I think Lippert purchased Kwikee a few years back.
Since the mechanical parts and motor are working and if your inspection of wires and connections being clean and tight are good under the step…….the only other thing is a flakey controller unit……but that’s just a WAG.