i have been botting for 2 months , there are few things as a newbie i found out that they can tell if all your accounts which are botted or not, if they really want to get into the details, in general it is the same for any other servers.
#private servers have anti cheats such as 'warden and änti cheat trinity"
1, they are monitoring network traffic which done by anti cheat, will give flags to accounts are botted
2,they can identify patterns of behavior that are typical of bots,such as spells and abilities in a specific order( running on heavly used fight classes will get your account a botting flag by anti cheat but not a ban yet if gm wasnt there)
3,they can tell if you are running on the same cumpter or not even using with proxy and vpn, they are able to collect your info with software from your computer such as installed fonts, hardware and software configurations, they are using the information to identify if multiple accounts are being controlled by the same machine,even with vpns.
4,they can tell if your account is botted through all kind of logs, such as chat logs(identify ad bots),gameplay logs( actions,locations,movements etc),inventory logs(when you got items and when ),combat logs(damage dealt and taken,healing done and taken)
5,they can tell account registrations are from your browser same as games are running from the same computer.
server admin can do all of above, if they really want to, sometimes they just dont have the time to get into details but simply ban those obvious accounts