I have a piece of wood clamped on a little stool, put a old big electric motor on the stool so it wont move and put the shifter on the plank. Have it there for more than 3 years now, works perfect.
You could try and make up some sort of bracket coming off your chair, I would try to make a nice simple one so you can dismount it easily when you want to!
I screwed a custom-built wooden platform into my desk, since my desk is hollow, it fell out recently (damn IKEA desk...), due to lack of support. My first idea was to clamp it, but then my father had the idea to screw it in. But now, I have it next to my wheel, until I come up with another way. (something is being thought of right now actually, Imma sketch it out..)
I'll edit this post to add an image of my wooden platform.
EDIT: took a quick image with my phone
I just remembered, I need to find a way to hold my joystick as a handbrake too, I'm tired if it being on an upside-down shelf..
I just went though finding something, and I did something similar to ACCAkut,
I went by home depot and picked up a 7 dollar clamp. Clamped it to the side of my desk at the height i wanted and the metal bar that sticks out, thats where my shifter goes. Has worked pretty well for me. Under harder driving, Ill add a small stool or some support under it so i dont feel like im going to snap the metal if i try to shift hard or go in reverse.