We propose a novel autonomous robotic palpation framework for real-time elastic mapping during tissue exploration using a viscoelastic tissue model. The method combines force-based parameter estimation using a commercial force/torque sensor with an ergodic control strategy driven by a tailored Expected Information Density, which explicitly biases exploration toward diagnostically relevant regions by jointly considering model uncertainty, stiffness magnitude, and spatial gradients. An Extended Kalman Filter is employed to estimate viscoelastic model parameters online, while Gaussian Process Regression provides spatial modelling of the estimated elasticity, and a Heat Equation Driven Area Coverage controller enables adaptive, continuous trajectory planning. Simulations on synthetic stiffness maps demonstrate that the proposed approach achieves better reconstruction accuracy, enhanced segmentation capability, and improved robustness in detecting stiff inclusions compared to Bayesian Optimisation-based techniques. Experimental validation on a silicone phantom with embedded inclusions emulating pathological tissue regions further corroborates the potential of the method for autonomous tissue characterisation in diagnostic and screening applications.