Say, I go on LOA for like a month or so. And I ask someone to take care of my account, by regularly logging into my account and getting XP, CPs etc, or simply to be online so then I can get faction income or whatnot.
If that person agrees to do so and then also does it in my absense, would he get banned? Or would I get banned? Or would I/he have to contact an admin and let the admin know ahead of time that this would go down?
If he would get banned for doing so, after how long would he get banned? Would he get banned after the first time he logs into my account? Or is it a period of time that determines the fate?
A quick review of the Spying Rules should answer your questions, but allow me to summarise:
The bottom line is that if you log into any other person's account for any reason, you will get banned as soon as it is detected. If you allow someone else to log into your account, chances are you're going to get banned too. Not even registered multis are actually allowed to access one another's accounts.
The length of the ban, and any additional punishments, can vary.
"May the Grace of Ara go with you, and His Vengeance be wrought upon your enemies."
This makes me glad that I declined a person's offer to investigate in a case where he was being accused a thief, and he wanted me to log into his account so I could have 'proof' that he did not steal (was like 1,5 years ago or so). I didn't do it, since someone told me back then that logging into someone else's account wasn't a good idea, but he did not tell me (probably because he didn't know himself) that I would get banned if I did. The person that was accused is banned or dead now anyway, but this is still good to know.