The 1/f resistance noise of a two-dimensional (2D) hole system in a high mobility GaAs quantum well has been measured on both sides of the 2D metal-insulator transition (MIT) at zero magnetic field (<i>B </i>= 0), and deep in the insulating regime. The two measurement methods used are described: <i>I</i> or <i>V</i> fixed, and measurement of resp. <i>V</i>or <i>I</i> fluctuations. The normalized noise magnitude S<sub>R</sub>/R<sup>2</sup> increases strongly when the hole density is decreased, and its temperature (<i>T</i>) dependence goes from a slight increase with <i>T</i> at the largest densities, to a strong decrease at low density. We find that the noise magnitude scales with the resistance, S<sub>R</sub>/R<sup>2</sup> ~ R<sup>2.4</sup>. Such a scaling is expected for a second order phase transition or a percolation transition. The possible presence of such a transition is investigated by studying the dependence of the conductivity as a function of the density. This dependence is consistent with a critical behavior close to a critical density <i>p</i>* lower than the usual MIT critical density <i>p</i><sub>c</sub>.