This paper presents an investigation of the discharge propagation (DP) to the readout electrode that occurs with a microsecond time delay after a primary discharge that develops inside a GEM foil hole. A single hole THGEM (THick GEM) foil that enables a controlled discharge position and the induction of primary discharge with an over-voltage in the THGEM foil has been used in the initial DP measurements. In order to justify the use of a custom-made THGEM foil, additional measurements were made with a standard GEM foil. Correlated optical (with an ordinary SLR and a high-speed camera) and electrical measurements of the delayed DP were made for Ne-CO$_2$-N$_2$ (90-10-5) mixture and with different powering configurations. Measurements show that the delayed DP happens without a drift field, with an inverted induction field, inverted THGEM voltages or an inverted drift field. After the primary discharge, there is a charge transfer in the induction region at an induction field value below that of the onset field for DP. In the time between the primary discharge and the delayed DP, three different current regimes are observed, which suggests multiple charge transfer mechanisms in the induction region. High-speed camera recordings provide valuable insight into the time evolution of the primary and the delayed DP, especially when correlated with electrical measurements.
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