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tokens: −1 . Observations of BG Ind were obtained simultaneously in two cameras on WASP-South over three observing seasons, from 2012 July 3 to 2014 December 6. Fluxes are measured in an aperture with a radius of 132 arcsec for the 85-mm data and instrumental trends are removed using the SYSRem algorithm (Tamuz, Mazeh Zucker 2005 ). Data points more than 5 standard deviations from a phase-binned version of the light curve were rejected and the entire night of data was rejected if more than one-fourth of the observations were identified as outliers based on this criterion. An 8-d section of the WASP measurements is shown in Fig. 2 . Note, we converted the original HJD(UTC) times of the WASP observations into BJD(TDT) for the forthcoming analyses. We also applied the same transformations for all the archival data that we describe below. Figure 2. An 8-d-long section of the WASP observations of BG Ind (blue circles). Red dots represent the best-fitting spectro-photodynamical model solution (see later, in Section 3 ) projected back to the epoch of each individual WASP measurement, while the black line shows the evenly phased model solution. The residuals curve is also shown below. 2.4 Other ground-based archive photometric data used for our analysis We downloaded publicly available Strömgren u, v, b, y photometric observations from the ESO archive (Manfroid et al. 1991 ; Sterken et al. 1993 ). These observations were carried out between JDs 2 446 581 and 2 447 069. The light curves in each bandpass contain 175 measurements. We used these data primarily to determine additional times of eclipses in binary A. Unfortunately, however, the majority of the nightly observations contain only a few measurements, and we were therefore able to determine the mid-times of only two primary eclipses (see below, in Section 2.6 ) from this data set. BG Ind was also observed by Jens Viggo Clausen and collaborators as part of their long-running observing programme to measure absolute dimensions for solar-type stars in eclipsing binaries, carried out since 1994 at the Strömgren Automatic Telescope at ESO, La Silla. Unpublished data and manuscripts that were in preparation from this observing programme have been made available to one of us (PM), from which we extracted five more eclipse times (see again, in Section 2.6 ). The observing procedures and data reduction for these observations are similar to those described in Clausen, Helt Olsen ( 2001 ). 2.5 Disentanglement of the light curves For the combined analysis of all the observational data, we used the original TESS time-series, i.e. the net light curve of the two binaries together. However, at the start of the analysis, we found it worthwhile to disentangle the light curves of the two binaries, so we could examine each one separately. We have described this process in substantial detail in Powell et al. ( 2021 ). Therefore, we review only the highlights here. First, we folded and binned the Sector 1 (i.e. Year 1) TESS SAP