The long range proximity effect in high-Tc c-axis Josephson junctions with a high-Tc barrier of lower Tc is still a puzzling phenomenon. It leads to supercurrents in junctions with much thicker barriers than would be allowed by the conventional proximity effect. Here we measured the T - x (Temperature-doping level) phase diagram of the barrier coherence length ξN(T, x), and found an enhancement of ξN at moderate under-doping and high temperatures. This indicates that a possible origin of the long range proximity effect in the cuprate barrier is the conjectured pre-formed pairs in the pseudogap regime, which increase the length scale over which superconducting correlations survive in the seemingly normal barrier. In more details, we measured the supercurrents Ic of Superconducting - Normal - Superconducting SNS c-axis junctions, where S was optimally doped Y Ba2Cu3O(7-δ) below Tc (90 K) and N was La(2-x)Sr(x)CuO4 above its Tc (<25 K) but in the pseudogap regime. From the exponential decay of Ic(T) ∝ exp[-d/ξN(T)], where d is the barrier thickness, the ξN(T) values were extracted. By repeating these measurements for different barrier doping levels x, the whole phase diagram of ξN(T, x) was obtained.