Should hyper-parameters used in the mutation operator be fixed or variable?

Let's say I have a function $$f(p_{i,t})$$ and want to optimize $$p_{i,t}$$ so that I minimize a certain loss. Here, $$p_{i,t}$$ is the individual $$i$$ at iteration $$t$$. Now, $$p_{i,t}$$ can live anywhere between 0 and $$N$$, where $$N$$ is a potentially large number.

The update rule for $$p$$ (or mutation operator) is given by

$$p_{i,t+1} = p_{i,t} + \eta \cdot \text{rand(-1, 1)}$$

I would like to know how to choose the step size $$\eta$$. Should it be fixed or variable? Should it be proportional to the parameter's magnitude? Is there any good reason to choose one over the other?