Keith's congruence conjecture for coefficients of a reciprocal false theta function

Let $c_5(n)$ be defined by

$$\frac{1}{\Psi(-q^5,q)}=\sum_{n=0}^\infty c_5(n)q^n,$$

where

$$\Psi(a,b):=\sum_{n=0}^\infty a^{n(n+1)/2}b^{n(n-1)/2}-\sum_{n=-\infty}^{-1}a^{n(n+1)/2}b^{n(n-1)/2}.$$

Keith's conjecture. For every integer $n\geq 0$,

$$c_5(32n+31)\equiv 0\pmod 8,\qquad c_5(128n+123)\equiv 0\pmod 8,$$ $$c_5(512n+491)\equiv 0\pmod 8,\qquad c_5(64n+19)\equiv 0\pmod 4,$$ $$c_5(256n+75)\equiv 0\pmod 4,$$

and, for $i\in\{110,138,194\}$ and $j\in\{19,47,75,103,159,187\}$,

$$c_5(196n+i)\equiv 0\pmod 4,\qquad c_5(196n+j)\equiv 0\pmod 4.$$

These congruences concern arithmetic progressions in the coefficients of the reciprocal of a false theta function. The conjecture was posed by Keith and is the result proved by the paper from which this candidate is extracted; the supplied parser status is unknown, so the database status remains open pending explicit resolution evidence.