JD1,
In all honesty I've got to tell you that your idea for an "adjustable support rod" to rest your hand on is (IMPO) a bad idea. It will simply become a crutch for you that besides limiting your range of smooth motion will hold you back from realizing your full potential (and versatility) at laying down long, smooth, high quality beads.
You need to learn to weld with only one hand on the gun. Trying to use your off-hand to steady the gun is seriously counter productive. Beside just burning that hand up (which is a lot of times the reason people have to stop welding before they've gone as far as they need to go or could have gone), more often than not it will only allow you to go only a short distance before it'll put you in a physical bind that'll cause you to have to stop the arc so you can reposition your hands.
Welding one handed is no where near as hard as most people seem to want to assume it is. Believe me it doesn't take any kind of super human strength or skill to do it. All though there's definetly some "tips and tricks" to doing it, it's much more of a mental game than any thing else.
Some of those "tips and tricks".....
As poster "hillbillyfab" has already alluded to in post #5, don't bear down or tense up in an effort to hold absolutely steady because that just makes things way worse (not to mention being extremely tiring over the course of the day). You need to keep your hand, fore and upper arm just as relaxed as possible and carry the weight of the gun in your shoulder and upper back.
Learning to use the trigger lock function is absolutely essential. If you have to hold the trigger down continuously while laying a bead it works against you in two ways. One, it causes some of the muscles in your forearm to have to remain tensed up and secondly it causes you to have to hold on to the gun tighter and in a limited number of ways. It'll rob you of at least 50% of the smooth range of motion of your wrist joint.
And a side note concerning "trigger lock".... If you ever run into some one who tells you that "trigger lock" is just for lazy, inexperienced welders who really don't know what they're doing well, do your self a favor and take every thing else they try and tell you about welding with a large degree of skepticism. Better yet, if circumstances allow, just tell them to go away because they're a f*ck'n idiot.