Are there rule of thumb regarding sample size when neuroscientific measurements are used?
The minimum sample size required to plausibly reject the null hypothesis depends not on the area of study (e.g. neuroscience), but on your study design and the statistical tests you perform.

What you need to do is a power analysis. Questions regarding power analysis have been asked on Cross Validated. You may want to read up on power analysis in your favourite statistics textbook and, if you have questions, ask them there.