Hi,
I have gone through the medical history of your dad and understood your concerns.
You say that he is getting depressed because his right arm only has a vein that bulges when he lifts it up and blood flows back down. When the arm is lowered, the vein disappears.
All these started in March and lots of tests resulted normal.
At the this point, there are few things you should explain to your dad regarding the anatomy of the blood vessels (veins in his case).
When the arm is lifting, the blood will flow back down and the vein is normally notable.
When the arm is lowered, the blood is not flowing back down, so no extra blood is added to the vein and it is not notable.
This phenomenon has been there for all your dad's life. My question is "why he noticed just now?".
Perhaps your dad has lost weight recently and was able to notice it.
Or perhaps, he might be suffering of aging
depression that should be further evaluated by
psychiatrist.
Anyway, the fact is that as long as all tests resulted normal, you should sit and explain your dad that this a normal phenomenon and normal anatomy of the blood vessels in the arms.
All the best.