Pseudorandom bit generator: analogue circuit for microcontroller digital input
Given that the degree of randomness is stated as not critical:

One random number generation mode that takes minimal resources is to read an open ADC pin within the code, and use the difference between one reading and its previous as a random number source. Make sure the ADC pin is not pulled high or low.

Using the differences eliminates any specific bias on the ADC pin, and provides a random sequence of zero-biased values. Depending on bit depth required, add up a series of such values if necessary.

The method lends itself to easy experimentation, so you can know pretty quickly whether the approach is providing sufficient entropy to meet requirements. If greater entropy is needed, connect an open wire to the ADC pin to provide greater sensitivity to external electric fields.