Left panel: orbital trajectories of a Galactic centre MSP with a_* = 825r_g, i = 76°, ω = Ω = π/4 and eccentricities e = 0.7, 0.8, 0.9 (blue, green, orange lines respectively). The scatter points are included as a reference for the right panels and label the initial, final, middle and superior conjunction sample points (turquoise, purple, brown, red respectively). The black cross labels the BH singularity. Right panels: propagation timing delay for each of the eccentric orbits, along with the errors between the PK and relativistic solutions (δ_α, i(Δ_prop), δ_β(Δ_prop)). For the middle two panels the dashed lines show the residual when the PK lensing correction is included (see also Fig. 5). Significant timing residuals are present between both δ_α, i(Δ_prop), δ_β(Δ_prop) relative to typical radio pulsar timing precision.