The closer you are to the equator, the taller the stick needs to be. If you're really close, the height requirements diverge, and the stick is at this point technically more of a space elevator[1] than a stick.

But don't lose hope, just tell Bezos that Musk wants to fund your space elevator, and vice versa, to goad one of them into funding your $10tn near-equatorial sundial boondoggle.

[1] https://en.wikipedia.org/wiki/Space_elevator