How does rudder size influence its ability to produce lateral lift?
The figure of 35% might be ideal for a rudder on GA aircraft with decent effectiveness and high enough control forces so a good control feel is achieved.

Generally, a rudder on a vertical tail is like a flap on a wing. It changes both camber and incidence of the vertical when deflected, thus helping the pilot to adjust the lateral lift force acting on the whole vertical. Therefore, the same formulas as those for flaps can be used for rudders.

A simple approximation for the amount of lift coefficient change per flap deflection angle $\eta$ is
$$c_{l\eta} = \sqrt{\lambda}\cdot\eta$$
where $\lambda$ is the relative chord of the flap and $\eta$ needs to be in radians.

Hermann Glauert derived a formula using potential flow theory that is sligthly more complex:
$$c_{l\eta} = c_{l\alpha}\cdot\frac{2}{\pi}\cdot\left(\sqrt{\lambda\cdot(1-\lambda)}+arcsin\sqrt{\lambda}\right)$$



I plotted both together with a correction of the Glauert formula using wind tunnel data above. It is remarkable how close the simple formula matches the experimental data already.

To be effective, the control forces on a rudder must not be too high, but also not too low in order to give good feedback to the pilot. For GA aircraft and gliders, a relative chord of 25 - 35% has been found to give the best combination. Control forces grow with the square of the relative chord of their control surface since both their area and the lever arm of the additional forces acting on them grow linearly with their relative chord.

In order to calculate the lateral lift change of the whole vertical, you need to know its lift curve slope $c_{l\alpha}$ which is affected by its aspect ratio and sweep angle, just like a wing is.