They don't "disappear". But depending on the nature of the banishment, they will either stop effecting your life or leave it entirely (IE: relocating, new job, new school, etc). Dark banishments can cause bad things to happen to them that cause them to leave. I prefer nicer banishments that give people opportunity elsewhere which is a mixture of luck and travel, or seperation spells that sever them from my life so they have no reason to be drawn to it any longer.
raven a banishment is a banishment. if you actually are forced to do a banishment, then its a tme to stop being nice and just do what ever it takes to get him/her/it out of your life.
Many years ago I had someone I wanted to get rid of. They were Christians from the Assembly Of God ( AOG ) who were able to talk in tongues. Other than their faith and being quite pushy, I had nothing against them in general. They were Jesus freaks you could say.
After many months of them coming around to nicely convert me to their way of life, I did a spell one night during that week to have them leave my life. I did not want my wife to know as she would have gotten quite upset about my rudeness to them. The spell was done at night when my wife was working night shift and I was alone in the house. It was not specific in the type of method used to make them leave. I cast a circle and summoned Satan to enter the property and do his thing to remove them. The spell was bit more than this, but you get the idea.
What happened; about a week later, they came over as usual for a social visit on the weekend and upon leaving late that night, the wife fo the couple said she saw a demonic form in the front garden bushes outside my house. It scared her and her husband so much they never returned again to visit. When I did eventually meet with them some months later, by "accident" you could say, they said my place was haunted with demons which were seen in the garden. They told me why they were not coming over again as a result of me lacking the holy spirit and my house was to them a dwelling place of demons.
My spell obviously worked by raising up their strongest fears and making it their reality. Being staunch A.O.G Christians who spoke in tongues - demons were one of their biggest fears.
So in my case I considered them banished and as a result they simply avoid you like the plague if the spell is effective. To banish anything you have to instil fear in the person. To do this you have to summon their fears into their life when they are around you. They quickly leave never to return when your objective is done correctly.