This is an important safety step and not being careful can risk electric shocks. Next remove the wires and track which are going into the fan section.

Bathroom Exhaust Fan Wired To Existing Light Fixture
How to separate bathroom fan and light switch. Connect two of the black. Bathroom fan with a light how to replace a double light switch how to install a bathroom fan with how to add a light bathroom fan to an existing light wiring a bathroom extractor fan with an isolator switchreplacing a bathroom light fan switch connections diynot forumshow to wire a 3 pole isolator switch diynot. The electrical wiring for separate switching of the bathroom exhaust fan and the light fixture will require identifying the existing circuit and existing switch wiring. Black should be the fan and red should be the light. Take the switch out of the wall box and check again that the power is truly off. Connect the two white wires in the switch box together with a wire nut.
The power source will either enter at the switch box or up at the light fixture or the exhaust fan. Splice the black wire from the fan together with the black wire from the light and the black wire from the switch and cap them. Turn off the circuit breaker controlling the bathroom you plan to work on. First youll need to turn off the circuit that delivers power to your fan and light. Attach the red and black wires from the fan light unit to the top terminal screws on the switches. Locate the switch cable which must be glued through the top or side of the box that serves the fan or the light.
Connect the black fan cable together with the black light wire and the black switch wire and cover them. The key factor is to understand where the power source enters the circuit. Using wire strippers strip an inch of insulation from the end of the black and white wires. We havent heard if red and white were tried at the light box because it sure looks like the switch is getting power which means red should also be getting power. The black passes thru that box and goes to the fan. Locate the switch cable which should be sticking through the top or side of the box serving the fan or light.
So if there is a separate fan. Using wire strippers peel an inch of insulation from the end of the black and white wires. Flip the light switch on and off to test preliminarily that the circuit is off. 2 mount a ladder or stepladder and remove. The three wire cable comes from the switches.