Electrical – Bathroom fan fluctuates in power when using countdown timer switch

Without running an additional switched hot lead, it can be done using radio frequency transmitting switches which control a RF receiver/relay which you would have to wire into the ceiling box. Leviton makes devices like that. They are neither simple nor cheap. In my opinion it would be easier, quicker, and cheaper to fish a new wire or even open the wall. Patching is painstaking and tedious but not difficult.

The diagrams below show how to wire the circuit. For simplicity I have not drawn in the electrical grounding conductors (green or bare Cu wires).

Note that the 2011 NEC introduced a requirement to provide a grounded conductor at the switch location (see this answer and this outside link for more details). You can avoid this requirement if you install the circuit before January 1, 2020 but there are good reasons to follow the new code if it's not unduly burdensome. You may upgrade the switches in the future with a smart switch that requires a grounded wire. Or you may need to branch off this box in the future to run additional switched or unswitched circuits.

For a pre-2011 NEC 3-wire install the switch loop can be run using Type NM-B 14/3 with ground. Re-identify the white conductor in the switch loop cable as ungrounded (on both ends) and connect to the ungrounded conductor from the branch circuit. Then connect the black and red wires as indicated in the diagram.

For a 2011 NEC 4-wire install the switch loop could be run using Type NM-B 14/2/2 with ground. Connect the grounded (neutral) wire from the branch circuit to the white wire in the switch loop. Connect the ungrounded wire from the branch circuit to the white wire with red stripes. Connect the black and red wires as indicated in the diagram. As I write this, it is hard to find 14/2/2 cable and often more economical to run a pair of 14/3 cables. In each case we are running an grounded (neutral) wire inside the cable that has the ungrounded wires for each switch loop. This is required by code to avoid inductive heating.

Prior to 2011 NEC

After 2011 NEC