  Aims: During its all-sky survey phase, the eROSITA X-ray telescope onboard
SRG scans through the ecliptic poles every 4 hours. This extensive data set of
long-duration, frequent, and consistent observations of thousands of X-ray
sources is ideal for a detailed long-term X-ray variability analysis. However,
individual observations are short, are separated by long but consistent gaps,
and have varying exposure times. Therefore, the identification of variable
sources, and the characterisation and quantification of their variability
requires a unique methodology. We aim to develop and evaluate such methods for
eROSITA observations, focusing on sources close to the survey poles.
  Methods: We simulate eROSITA-like light curves to evaluate and quantify the
effect of survey mode observations on the measured periodogram and normalised
excess variance. We introduce a new method for estimating the normalised
intrinsic variance of a source based on the Bayesian excess variance (bexvar)
method.
  Results: We determine thresholds for identifying likely variable sources
while minimising the false-positive rate, as a function of the number of bins,
and the average count rate in the light curve. The bexvar normalised intrinsic
variance estimate is significantly more accurate than the normalised excess
variance method in the Poisson regime. At high count rates, the two methods are
comparable. We quantify the scatter in the intrinsic variance of a stationary
pink noise process, and investigate how to reduce it. Finally, we determine a
description of the excess noise in a periodogram caused by varying exposure
times throughout a light curve. Although most of these methods were developed
specifically for analysing variable AGN in the eROSITA all-sky survey, they can
also be used for the variability analysis of other datasets from other
telescopes, with slight modifications.
