In the search for an electron antineutrino detection method with sensitivity below the 1.8 MeV threshold for the inverse beta decay reaction, beta decay counting experiments with ca. 3 kBq 22Na and 60Co sources were conducted at unit #1 (2.775 GW_th) of the Koeberg Nuclear Power Station in South Africa. The setup consisted of one NaI crystal to measure de-excitation and annihilation photons associated with beta decay. Its volume and well shape were chosen to use coincidence summing in order to differentiate between electron capture and beta+ emission in 22Na. The setup was shielded from the reactor core by 8 m of uninterrupted concrete. Background radiation, responsible for ca. 1% of the total countrate with either source, increased by merely 3% when the reactor status changed from OFF to ON. Normalized countrates of three energy regions-of-interest (TOT, MED, HI) were parameterized to jointly describe the time dependence of two instrumental effects and a reactor-status step function in a least-squares regression analysis. With the 22Na source, the fractional countrate changes in the step from reactor OFF to ON were: (delA/A)_TOT = [-3.02 +- 0.14(stat) +- 0.07(syst)] x 10^-4, (delA/A)_MED = [+1.44 +- 0.42(stat) +- 0.07(syst)] x 10^-4, and (delA/A)_HI = [-2.70 +- 0.26(stat) +- 0.04(syst)] x 10^-4. The uncertainty budget is incomplete because it does not contain the possible influence from environmental factors and the finite stability of the MCA clock-oscillator. No reactor-status dependence was observed with the 60Co source. The corresponding cross sections are [1.55 +- 0.07(stat)] x 10^-25 cm^2 for EC + beta+ decay in 22Na and [0.5 +- 1.5(stat)] x 10^-26 cm^2 for beta- decay of 60Co. The negative sign for TOT and HI activity changes in 22Na points to an antineutrino related interference effect on the beta+ decay of 22Na and rules out reactor neutron induced reactions.