The influence of randomly quenched disorder in the incommensurate phases of Rb-2(Zn1-xCux)Cl-4 (for x = 0.03), Rb-2(Zn1-xCdx)Cl-4 (for x = 0.03 and 0.05), Rb-2(Zn1-xHgx)Cl-4 (for x = 0.03 and 0.05) and Rb2Zn(Cl1-xBrx)(4) (for x = 0.01 and 0.03) is investigated via the amplitudon and phason dynamics using Cl-35 nuclear quadrupole resonance studies. Defect pinning at the metal and halogen sites in the prototype compound Rb2ZnCl4? has been attempted for the first time and has yielded novel results. Quenched randomness at the metal site (Zn) in Rb2ZnCl4 induced strong pinning of the modulation wave (irrespective of the size of the dopant compared to the host). This is evident from a temperature-independent Delta(phi) and consequently T-1 phi unlike the case for impurity pinning at the other sites (cation and anion). The effect is enhanced with increasing concentration of the dopant. This result is contrasted with defect pinning at the halogen site (Cl) in Rb2ZnCl4 with Br substitution which induced weak pinning of the modulation wave (temperature-dependent Delta(phi) and consequently T-1 phi) similarly to substitution at the cation site as seen from earlier studies. Furthermore, the impurities have been categorized as random-field or random-potential type by evaluating the symmetry parameter (m) associated with the impurity. It is seen that Cu, Cd and Hg are random-field-type impurities inducing strong pinning of the modulation wave (m < 6; m = 6 for Rb2ZnCl4) while the Br impurity is of a random-potential type inducing a weak pinning of the modulation wave.