Shimano 105 right 9 speed shifter problem

Hi All,
First let me say I'm new to the forum, and have really enjoyed reading many for the threads over the past few days. I have a lot to learn!
I'm having a problem with my right side shifter when shifting to a higher gear.
It's a Shimano 105 5500 9 speed brifter.
First let me say that shifting with the large lever, ( small cog to bigger cog) works fine, but when I try to shift with the small lever, (big cog to smaller cog) the large lever moves with the smaller lever and the gears don't change. There's no click or anything. Both levers move over and just stay there until I move them back. I can however, shift with the small lever if I hold the large lever in place. Then everything works fine through the whole range.
I'm hoping someone has run into this before and can advise me on what the problem is, and whether or not it's repairable.
I'm fairly handy, but after watching a few Youtube videos that show how to disassemble the shifter, I don't think that's a project I would like to take on unless I know what I'm looking for.
I have already thoroughly cleaned the shifter with WD40, and the problem exists whether or not there is tension on the cable.

Thanks in advance for any help.
Jeff