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We have experimentally studied the persistent photoconductivity (PPC) in inverted InAs/GaSb and InAs/GaInSb quantum wells, which can be tuned into a bulk-insulating state by electron-hole hybridization. Specifically we tune the bulk band structure and carriers with light-emitting diode (LED) illuminations. The persistent photoconductivity could be negative or positive, depending on the specific doping structure and the illuminating photon energy. Compared to the widely-used electro-statically gating method, our findings provide a more flexible and non-invasive way to control the band structures and charge states in InAs/GaSb and InAs/GaInSb quantum wells (QWs).