You are correct in deducing that you can tap into the incoming hot line in the light switch box. It appears that the hot line comes in from either the lower cable or the cable on the upper right in the picture. The cable on the upper left seems to go to the existing light fixture.
You need to connect the hot cable from the bundle of black wires to the hot side of the new switch. You can use a pigtail (short length of wire). Then connect the new black line to the vent to the other side of the new switch. You also need to add the white wire from the vent to the existing bundle of white wires in this box.
The simplest way to handle this might be a double switch that fits within a single gang box.
The one shown is decorator style but these are available in several styles. If you go this route, you replace the current switch. You move the black wire currently on the old switch to one of the common hot terminals on the new switch. You can tell which it is by the metal tab connecting the two adjacent terminals. This allows both switches to share a hot using only one wire. You leave the other common terminal empty (but screw it in for safety).
You then attach the other wire that currently goes to the light (the remaining wire from the old switch) to one of the opposite terminals on the switch and the new hot line for the vent to the final opposite terminal.
Safety: Be sure to turn off the breaker before touching any wire or terminal, and confirm no power using a non-contact tester or multimeter. Your cables, switches and fixtures should be grounded, but no ground wire is visible. It may be that your system is grounded through armored cable or conduit, or it is on an ungrounded GFCI line. I would add a ground wire from both the switch and the new vent wire to a screw in the back of the box.
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