What is the spell save DC for this magic item from Waterdeep: Dungeon of the Mad Mage?

Question

There is an item in the Waterdeep: Dungeon of the Mad Mage adventure, the

black crystal tablet

described on p. 284. Its description states:

As an action, a creature attuned to the black crystal tablet can use it to cast eyebite...

However the eyebite spell states:

One creature of your choice within 60 feet of you that you can see must succeed on a Wisdom saving throw or be affected by one of the following effects of your choice for the duration...

What is the spell save DC used when casting this spell?

Note that the entire description of the item (provided below) does not list a save DC to use when casting spells from it:

The black crystal tablet is a legendary magic item that requires attunement by a creature that has proficiency in the Arcana skill. Any creature that attunes to the tablet must make a DC 20 Wisdom saving throw at the end of its next long rest. On a failed save, the creature becomes afflicted with a random form of long-term madness (see "Madness" in chapter 8 of the Dungeon Master's Guide).

As an action, a creature attuned to the black crystal tablet can use it to cast eyebite or gate (the portal created by this spell links to the Far Realm only). After the tablet is used to cast a spell, it cannot be used again until the next dawn.

It is notable that this item does not require you to be a spellcaster to attune to it, so even creatures without spell save DCs could attune to it.

Answer 1

Use your own Spellcasting DC

As stated in the Dungeon Master's Guide, unless a magic item says what its save DC or attack modifier is, you use your own Spell Save DC/Attack modifier

Spells

Some magic items allow the user to cast a spell from the item, often by expending charges from it. The spell is cast at the lowest possible spell and caster level, doesn’t expend any of the user’s spell slots, and requires no components unless the item’s description says otherwise. The spell uses its normal casting time, range, and duration, and the user of the item must concentrate if the spell requires concentration. Certain items make exceptions to these rules, changing the casting time, duration, or other parts of a spell.

A magic item, such as certain staffs, may require you to use your own spellcasting ability when you cast a spell from the item. If you have more than one spellcasting ability, you choose which one to use with the item. If you don't have a spellcasting ability - perhaps you're a rogue with the Use Magic Device feature - your spellcasting ability modifier is +0 for the item, and your proficiency bonus does apply.

But I don't have a Spellcasting DC

See the very last sentence of the quote above.

If you don't have a spellcasting ability - perhaps you're a rogue with the Use Magic Device feature - your spellcasting ability modifier is +0 for the item, and your proficiency bonus does apply.

This clearly states that if you are able to use a magic item that would normally require you to use your own Spellcasting Ability to cast it, despite not having a Spellcasting Ability, then your Ability Modifier is +0, but you still get to use your Proficiency Bonus.

Thus, if someone who does not have a specific Spellcasting Ability uses that item to cast its loaded spell, the Save DC will be 8 + Proficiency. (Computed with the standard 8 + Ability Mod + Proficiency)

To cover something you asked in a comment...

"Spellcasting Ability" and "Ability to cast spells" are two different things. The ability to cast spells (such as being a Totem Warrior Barbarian) does not mean you have a Spellcasting Ability. "Spellcasting Ability" is a specific term used to refer to which Ability Score (Wis, Int, Cha) is used to power your spellcasting.

So a Totem Barbarian would be stuck with the same rules. They don't have a specific Spellcasting Ability, despite being a spellcaster. Thus, they use 8 + Proficiency for their Saves.

In conclusion

If you have a specific Ability you use to power spellcasting (whether that's from the Spellcasting class feature, a Feat, a racial spell, etc.) you may use that ability modifier to determine the Save DC of a magic item. If you do not have a specific Spellcasting Ability, you use 8 + Proficiency to calculate the save DC.

Answer 2

The Dungeon Master's Guide, Chapter 7, under "Activating An Item" and "Spells" states the following:

Spells

Some magic items allow the user to cast a spell from the item, often by expending charges from it. The spell is cast at the lowest possible spell and caster level, doesn’t expend any of the user’s spell slots, and requires no components unless the item’s description says otherwise. The spell uses its normal casting time, range, and duration, and the user of the item must concentrate if the spell requires concentration. Certain items make exceptions to these rules, changing the casting time, duration, or other parts of a spell.

A magic item, such as certain staffs, may require you to use your own spellcasting ability when you cast a spell from the item. If you have more than one spellcasting ability, you choose which one to use with the item. If you don't have a spellcasting ability - perhaps you're a rogue with the Use Magic Device feature - your spellcasting ability modifier is +0 for the item, and your proficiency bonus does apply.

So I believe that you would use your own spell save DC, based on the guidance in the second paragraph.