This is quite doable, without putting anything but the outlet, assuming that there is a completely separate connection to the integrated switch. As far as I can tell, most of these combo outlets have two wires coming out the back for the switch, as well as four terminals for the GFCI outlet; If your combo outlet/switch does not have that, then get a different one.
First, DO NOT USE the LOAD terminals on the GFCI!
Connect the incoming HOT (black) wire to all of the following: the GFCI hot LINE terminal, one wire to the integrated switch and the line terminal/wire of the timer. Use a wirenut or Wago-type connector to connect everything together; don't try to put multiple wires under the GFCI's terminal.
Connect the switched hot (black) to the light to the other wire from the integrated switch.
Connect the load terminal/wire from the timer to the switched hot (black) going to the fan.
Connect together all of: the incoming neutral, the neutral return from the light and the neutral return from the fan. If the timer has a neutral wire/terminal, connect that too. All of these wires should be white.
Connect together all grounds, including ground pigtails to the combo and the timer.
Because you didn't use the LOAD terminals on the GFCI, you won't have the problem of the lights going out if you pop the GFCI.
enter image description hereI have an existing double gang box in my bathroom that contains a gfci/switch combo and a single pole switch. The switch on the gfci controls the exhaust fan and the single pole switch controls the light. I want to rewire the box where the gfci/switch combo can be used to power the light with theb outlet having constant power and add a countdown timer to control the exhaust fan. I have 12-3 coming in with the red wire being hot and 12-2 going out to the exhaust fan. If anyone can break down or walk me through the wiring diagram, I would be grateful.
