1/8" tube is way overkill. Use 0.065" and add a couple more braces. My preference is for 2"x0.065" square tube.
I guess I don't know much about framing. I thought if I used the 1/8" wall tube that is overkill I would not need to add the suggested braces.
My question is, what is the horizontal strength of the tube?
I think the general consensus is 1/16 steel tube is strong enough.