I think Standardized Precipitation Index (SPI) is good fit with your objective. The SPI value is spanning from -3 to +3, positive SPI values indicate greater than median precipitation (Wet) and negative values indicate less than median precipitation (Dry).
You can read the official guideline from WMO here: http://www.wamis.org/agm/pubs/SPI/WMO_1090_EN.pdf
For simple calculation, use this: https://www.calculatoratoz.com/en/optimum-number-of-rain-gauge-stations-calculator/Calc-5418
You need to know the CV and degree of error (example: 10%).
CV can be calculated from average and stdev of monthly rainfall in certain area. The equation is CV = 100*stdev/avg.
Then number of optimum rain gauge will be N = (CV/error)^...