If you have telepathy, you should hear the quest leader’s telepathic summons message more clearly than its current garbled state (perhaps “m..ic transporter”), and if you have extrinsic telepathy, you should hear it with perfect clarity.

Telepathy currently sees things with minds. Change it (or perhaps change only the amulet of ESP, leaving other telepathy the same) so that it sees things with souls instead of minds. Mostly this corresponds with the same monsters (with a few exceptions such as mummies which are animated by the soul of the dead person), but if a monster with a soul is polymorphed into a form that normally doesn’t, it retains its original soul, and shows up as its original form to ESP.

Additionally, ESP shows the spirit of a humanoid with a soul just after you kill it if you’re blind, making some angry or resigned gestures before fading away.

Amulets of ESP occasionally randomly cause a detect unseen effect, because extra-sensory perception is more than just telepathy.

Monsters can wear amulets of ESP. This allows them to know your exact location (regardless of invisibility or displacement) when you are within the telepathy radius.