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TheβPictoris system is the closest known stellar system with directly detected gas giant planets, an edge-on circumstellar disc, and evidence of falling sublimating bodies and transiting exocomets. The inner planet,βPictoris c, has also been indirectly detected with radial velocity (RV) measurements. The star is a knownδScuti pulsator, and the long-term stability of these pulsations opens up the possibility of indirectly detecting the gas giant planets through time delays of the pulsations due to a varying light travel time. We search for phase shifts in theδScuti pulsations consistent with the known planetsβPictoris b and c and carry out an analysis of the stellar pulsations ofβPictoris over a multi-year timescale. We used photometric data collected by the BRITE-Constellation, bRing, ASTEP, and TESS to derive a list of the strongest and most significantδScuti pulsations. We carried out an analysis with the open-source python package maelstrom to study the stability of the pulsation modes ofβPictoris in order to determine the long-term trends in the observed pulsations. We did not detect the expected signal forβPictoris b orβPictoris c. The expected time delay is 6 s forβPictoris c and 24 s forβPictoris b. With simulations, we determined that the photometric noise in all the combined data sets cannot reach the sensitivity needed to detect the expected timing drifts. An analysis of the pulsational modes ofβPictoris using maelstrom showed that the modes themselves drift on the timescale of a year, fundamentally limiting our ability to detect exoplanets aroundβPictoris via pulsation timing.