Second picture: To me looks like Q1 (3400) is an NMOS which connects the LEDs to power. The ‘gate’ is marked yellow. It is the ‘control’ input of the MOSFET. The 4 resistors RD RC RB RA (purple) probably limit the current through the LEDs. If you’re lucky, then an easy hack would be to bypass this transistor: Remove Q1 and connect the red and green marks via a mechanical switch. You’d need to scratch away the white coating until you get copper. Then solder wires there. As a consistency check you could measure the voltage over Q1 (red and green marks). Measure once when the module is plugged in but switched off, and once when the LEDs light up. If you see a voltage while the LEDs are dark, then this would partially confirm my guess. As a test: Before removing Q1 you could also try to bypass Q1 with a resistor (~ one, two kOhm) while the LEDs are off. If you see LEDs now lighting dimm, you know that Q1 is the one switching the LEDs.
Other possibility: It might possible that the timeout is computed with an R-C circuit. for 30min you need a rather large resistor because there can’t be very big transistors. R1 (blue) is the largest one. Experiment could be to remove it and see if timeout is still 30min. Or put another 10k resistor in series and see if the timeout gets shorter.
Wondering: What voltage do you connect to the module? Please be extra careful if you have somewhere mains supply voltage.