I caponized eight barred rock cockerels today.  All eight are full capons, and I removed both testicles through one incision on the bird's right side.  
 
I removed the right testicle first (the one closest to the incision) and then I removed the left testicle (the one furthest from the incision).
 
In many cases, I couldn't see the left testicle as I looped the wire tool around it.  I checked with the paddle probe to be sure it was there, but the actual taking of the testicle was done more by feel than by sight.
 
Full capons.  No slips.  No losses.  No pictures.  I set up my video camera but one of the barn cats kept rubbing against the tripod.  We shared words and decided it was best to put the video camera away before it was broken.  I attempted to wear my iPhone5 on my forehead.  The battery died, but I don't know when that happened, so maybe there will be some usable video footage.  
 
This is a turning point for me.  I think beginners will benefit from making an incision, removing the close testicle, turning the bird, making a second incision, and removing the second testicle.  Doing this over and over will make the operator familiar with the correct incision site, removal of the testicular membrane, and correct use of the wire tool.  AFTER one is proficient and confident, then removing both testicles through the bird's right side is the next logical step in training.  Avoiding the artery between the kidneys, not damaging the kidneys, avoiding large blood vessels; these things take practice.  If you're learning to caponize, don't beat yourself up over not being able to find both testicles through one incision.  Learning takes time.