I have always ran two accounts on the same ip aswell, while doing ess and while not doing ess. Never been banned. But once I signed in after this update I get banned. Just advice pal. Do what you would like, but I am pretty sure they are looking out for people with multiple accounts running. Since Jagex only wanted players to run one account at a time to begin with because of gold farmers.
I literally just logged onto my gold farm account just now while im signed into my main on my other client and I played for 2 mins trying to get back to the place to farm on Pure essence and I get logged and Perma banned... I highly advise nobody opening up two accounts atm just because they are trying to bot bust! BE CAREFUL!