Gap width slider does work, it's all about how your data are organized.
Your data are now grouped in columns, and each column will represent a new series in the B&W chart.
That is however not the proper way for these kind of charts.
You need to set your data in one single column, with an additional column for the group labels so excel can distinguish between groups and create separate boxes.
Select the data in the two columns and create your B&W chart.
When this is done you will also see the different group names on the horizontal axis, which you couldn't before because there was only one group (with three separate series). That's the tiny number you see above "Axis title" on your charts.
Chart A and B show different settings on gap width, with different result as you can see.
Your original problem is shown i chart C and D. Here I have added another series (orange) to demonstrate your previous cluster of three series. When you use gap width, the distances changes between those clusters, but NOT between series. The gray boxes illustrate this. You only saw what was inside this imaginary gray box since you only have one group per series. it appears that the distance to either side changes, but not between boxes. And that's true. Changes are between groups not series.
Change your data input and it will work.