The mask museum in Kirishima was called “Tengu-kan”, and obviously there were a lot of masks of tengu on display. Most of which were the red-faced long nose variety.
Probably the earlier version of Tengu was more birdlike in appearance, like the one in the top center of the photo below. The long nosed version is probably derived from Sarutahiko, the earthy kami who helped lead Ninigi and his entourage from the High Plain of Heaven. he later married Uzume and a mask of Sarutahiko and Uzume are often found together at shrines, often linked to fertility.
Tengu are often connected to Yamabushi, the mysterious mountain monks who practised austerities and magic in the remote sacred mountains. A distinguishing feature is the tokin, the small black headgear worn on the top of the forehead. It is said this was to protect the head while walking through the forest. It was also used as a drinking vessel.
The museum is located near the entrance to Kirishima Jingu Shrine up in the mountains of northern Kagoshima and if you are visiting the area and like masks then is a must see.