Rumormonger's rivere adds one 4th lvl spell slot to beguilers.
I would expect putting it on would add one 4th spell for free, so if you had 4 spell cast, putting it on should give you a 5th. What it does instead is that not only it wont add any spell, but when you remove it, it takes away a spell slot each time.
way to reproduce:
- rest
- wear the necklace, check the number of spells available
- remove the necklace, check the spells available again
- rinse and repeat a few times