Comet 162P/Siding Spring is a large Jupiter-family comet with extensive archival lightcurve data. We report new r-band nucleus lightcurves for this comet, acquired in 2018, 2021 and 2022. With the addition of these lightcurves, the phase angles at which the nucleus has been observed range from 0.39{deg} to 16.33{deg}. We absolutely-calibrate the comet lightcurves to r-band Pan-STARRS 1 magnitudes, and use these lightcurves to create a convex shape model of the nucleus by convex lightcurve inversion. The best-fitting shape model for 162P has axis ratios a/b=1.56 and b/c=2.33, sidereal period P=32.864+/-0.001h, and a rotation pole oriented towards eclipitic longitude {lambda}E=118{deg}+/-26{deg} and latitude {beta}E=-50{deg}+/-21{deg}. Using the shape model to correct the lightcurves for rotational effects, we derive a linear phase function with slope {beta}=0.051+/-0.002mag/deg and intercept Hr (1,1,0)=13.86+/-0.02 for 162P. We find no evidence that the nucleus exhibited an opposition surge at phase angles down to 0.39{deg}. We constrain the possible nucleus elongation to lie within 1.4<a/b<2.0 and discuss tentative evidence that 162P may have a bilobed structure. The challenges associated with modelling the shapes of comet nuclei from lightcurves are highlighted, and we comment on the extent to which we anticipate that LSST will alleviate these challenges in the coming.