It is difficult to track an FM transmitter because the FM radio's modulated sound is always at the same level regardless of the signal strength (if the radio is good).
An AM transmitter that is received on an AM radio has its modulated sound fading when the signal strength is low and the sound level increases with increased signal strength so an AM radio needs to have automatic-gain-control.
There is an FM tracking circuit on the internet that rapidly switches two antennas. When the signal on each antenna is the same level then they add. When the signals are so that one antenna is close and the other antenna is farther from the transmitter then the signals cancel. The problem of not knowing if you are facing the transmitter or if it is behind you is solved by adding some phase shift.
You need to make sure the receiver is well shielded. When you are close to the transmitter, the signal can be picked up by the receiver circuit board directly if it is not shielded and then you lose all of the directional value of your antennas. Prevent this by putting the receiver into a metal box.
There is an FM tracking circuit on the internet that rapidly switches two antennas. When the signal on each antenna is the same level then they add. When the signals are so that one antenna is close and the other antenna is farther from the transmitter then the signals cancel. The problem of not knowing if you are facing the transmitter or if it is behind you is solved by adding some phase shift.
Amateur radio operators and others participate in fox hunts (there are probably other names for this activity). You might google there.
In amateur radio handbooks there are relatively easy to build attenuators that might improve the usefulness of a normal FM receiver given the concerns expressed in audioguru's comment.
A reflected signal might confuse or complicate your direction finding efforts.