Sorry, when I said SMC, I meant Surface Mount Component. I am enclosing a pic. The two left-hand lines coming down from the battery + terminal, both go to the upper terminal of what was Q1H. The two right-hand lines go up to the edge connector feeding the camera board. The left-hand terminal of QH1 feeds the LED board.
I'm afraid there is absolutely nothing left of Q1H to show.
The circuit topology and footprint suggest a MOSFET in a SOT-23 or similar package connected as a high- or low-side switch, with a signal on the bottom left terminal controlling current between the two wider traces. Gate on bottom left, drain on top and source on bottom right would match the pinout of common FETs such as NDS0610 (P-channel) or 2N7002 (N-channel). A P-channel FET as a high-side switch seems obvious, but there's a 100K resistor (R1H) to ground on the "gate". This weak pull-down would force a P-FET on at all times unless the control circuitry dictated otherwise.
You could test this theory by shorting the top and bottom right pads with external power disconnected. The camera should then operate normally from battery power. No guarantees, usual disclaimers apply.
You can also test for voltage across R1H while the camera is operating from external power. Presence or absence of voltage will provide a clue to the circuit's functionality. If you can provide high-resolution photos showing the rest of the board, particularly where the traces connected to Q1H end up, that would also be helpful.