  We present the analysis of a total of 177h of high-quality optical
time-series photometry of the helium atmosphere pulsating white dwarf (DBV) EC
20058-5234. The bulk of the observations (135h) were obtained during a WET
campaign (XCOV15) in July 1997 that featured coordinated observing from 4
southern observatory sites over an 8-day period. The remaining data (42h) were
obtained in June 2004 at Mt John Observatory in NZ over a one-week observing
period. This work significantly extends the discovery observations of this
low-amplitude (few percent) pulsator by increasing the number of detected
frequencies from 8 to 18, and employs a simulation procedure to confirm the
reality of these frequencies to a high level of significance (1 in 1000). The
nature of the observed pulsation spectrum precludes identification of unique
pulsation mode properties using any clearly discernable trends. However, we
have used a global modelling procedure employing genetic algorithm techniques
to identify the n, l values of 8 pulsation modes, and thereby obtain
asteroseismic measurements of several model parameters, including the stellar
mass (0.55 M_sun) and T_eff (~28200 K). These values are consistent with those
derived from published spectral fitting: T_eff ~ 28400 K and log g ~ 7.86. We
also present persuasive evidence from apparent rotational mode splitting for
two of the modes that indicates this compact object is a relatively rapid
rotator with a period of 2h. In direct analogy with the corresponding
properties of the hydrogen (DAV) atmosphere pulsators, the stable low-amplitude
pulsation behaviour of EC 20058 is entirely consistent with its inferred
effective temperature, which indicates it is close to the blue edge of the DBV
instability strip. (abridged)
