Maximum number of options when selected via next and previous buttons?

I'm designing a product that has customizable features. The user can customize a light color by pushing a forward (>) or back (<) button. This action will toggle through a set color palette that will loop back once they reach the end.

I'm setting it up so that holding either button (< or >) will jog more quickly through the color options, but assuming the user is unaware that holding the buttons will run through them quicker...

And regardless of how many colors a user can distinguish or even needs...

How many options (aka. button presses) is enough before the user gets frustrated by toggling through them all? Any experience or studies to support this?

It's safe to assume that toggling through 3 colors would not be annoying. However, toggling through 1,000 colors could be. I'm wondering if there's some "sweet spot" in between.

[edit]

To clarify these are physical buttons on a physical product.

[edit 2]

I don't follow how seeing an example helps gauge user frustration, but there have been enough requests so here's a rudimentary mockup. The buttons change the color of the light below.

The example I used was color, but it may as well be something else (like sounds, projected symbols, etc.). The question still stands with how many options are too many before the user gets frustrated.