A brighter bulb in the room's light fixtures may be your solution.

I would swap out the wood shelves for glass ones. That is typically what people do who want to light the inside of their cabinets. It's an easy solution to making sure the light is throughout the cabinet.

But just make sure you even want to do this. A couple of kitchens ago I installed lighting inside some upper cabinets. After the novelty wore off in a few days, I never turned them on. It was an expense that I could have better used on something else in my kitchen.

In one of my frameless showroom sales displays, we did tape light on the sides. We had to slightly notch the shelves, but you can barely tell...and when the doors are closed, you can't really see the tape light.

@The Kitchen Place -

Thank you thank you thank you! What a clear example of how to make this happen. The result looks wonderful.

It looks like the tape light runs underneath the gaps in the hinges, so it must have been installed before the hinges were added to the doors?

You are most welcome! :-) The cabinets came with the doors on them. My install guy probably removed the doors to do this and put them back on when it was done. I don't really remember....it's been a few years and I didn't watch him do it.

"It looks like the tape light runs underneath the gaps in the hinges, so it must have been installed before the hinges were added to the doors? "

No, the hinges were most likely already there when the LED tape was installed. Frameless cabinet doors use European hinges like the ones shown in The Kitchen Place's photos. When you take the kitchen cabinet door off of this type of hinge, the hinge arms stay with the door. I.e. once the door is removed, that crosspiece you are seeing (the hinge arm) where the tape as you put it is "running underneath" is not attached to the cabinet side. The hinge arms stay with the door. The hinge mounting plates that are screwed into the cabinet side and into the door side of course remain in place.