How does a TACAN signal change with bearing from the station?
Change in bearing doesn't change frequency. The ground station always transmits  pulses on a single assigned frequency. The illustrations in the link from @CrossRoads only show what would be seen by a receiver at 000 magnetic. For other bearings the whole envelope shifts while the reference bursts stay still. The antenna illustration shows reflectors on spinning drums that create an envelope whose phase difference from the reference bursts depends on bearing. My markup of the diagrasms in the link (MRBs are blue):