I would like to flip a toilet handle 180 degrees for tank clearance with a side vanity. How can I remove just the handle from the rod? (there is a small hole that looks like it has something to do with this just on the backside of the handle). See the picture below.

There shouldn't be a vanity that close that it affects the handle.

Well, there is.

Due to the very small size of the bathroom the only option is to flip the handle.

Any hints or suggestions? (other than getting a bigger bathroom?)

Get a new toilet with a push button on top of the tank

You might try the Korky or Fluidmaster universal fit/adjustable tank lever

[a.co]

Steve's right: there has to be 15 inches from the center line for the toilet. Unless you have a 30-inch wide tank you're not code-compliant. I recently renovated my bathroom, have no room for a vanity, so installed a wall-hanging sink. That'd be the way you could make your bathroom work. You may not care, but if you sell the place a buyer or their inspector may.

I also need an unusual toilet lever, have tried to take mine apart. I couldn't. They're cheap, not made for customization. Perhaps someone sells a high-end model, not on the shelf at BigHomeStore or hardware stores, that can be taken apart.

My Father-in-law built a house about 1975 with a matching pink cast iron tub and wide tank toilet. The flush lever was a round plastic knob with a very short arm. A nylon string was attached to the end of the arm and directed through a guide on top of the overflow to the flapper. You could turn the knob one turn in either direction to lift the flapper. When he passed, my nephew bought the home and the first thing to go was the pink fixtures.