Sign-change conjecture for Birch–Erdős representation functions

Let $f_{p,q}(n)$ be the Birch–Erdős representation function, with $p$ and $q$ relatively prime integers satisfying $q>p>2$. Sign-change conjecture. The sign of

$$f_{p,q}(n+1)-f_{p,q}(n)$$

changes infinitely often. The conjecture is presented as a possible example of the Chebyshev bias phenomenon; the source does not establish it.