Will an Amulet of Proof against Detection and Location protect an invisible character from being observed directly with divination magic?

I get that the Amulet would prevent the wearer from being detected by location/scrying type spells, but would it also protect them from being detected in ordinary line-of-sight by somebody with an effect that would allow them to see invisible, like Truesight or wearing a Robe of Eyes?

From the description of the item:

While wearing this amulet, you are hidden from divination magic. You can't be targeted by such magic or perceived through magical scrying sensors.

Does being looked at by somebody who can see invisible creatures count as being the "target" of the magic?

No, it will not protect from standard True Sight or the Robe of Eyes

The Amulet of Proof against Detection and Location only says that you are:

hidden from divination magic. You can't be targeted by such magic or perceived through magical scrying sensors.

Not divination magic or magical scrying sensors

Standard Truesight and the Robe of Eyes just allow you to see Invisible creatures. There is no divination magic involved and neither are Magical Scrying sensors - they are just things that provide the ability to see invisible creatures.

It's all about the source of True Sight/seeing invisible

It would work against True Sight delivered via the spell True Seeing as that is specifically divination magic which the amulet protects against.

If the source of whatever gives a creature the ability to see invisible is directly associated with divination magic or magical scrying, then it would work. But that connection must be explicitly stated in order for it to work.

You are protected from divination spells and magical scrying sensors.

Both True Seeing and See Invisibility are divination spells, so they would have no effect.

Senses that are natural (ancient dragon's natural truesight) or granted by items are not considered spells, and thus you are not protected from them (unless the item specifies you are using it to cast the spell, or is based on scrying). Using your example, Robe of Eyes wouldn't be affected by the amulet.

Looking at someone counts as "targeting" them (according to Jeremy Crawford)

Going purely by the rules as written, it's not clear whether protection against targeting by divination spells would protect you from spells that the caster casts on their self that then grant new senses, such as see invisibility or true seeing. However, Jeremy Crawford has clarified on Twitter¹ that in such cases, you are still protected:

The nondetection spell hides you from divination magic. True seeing is a divination spell.

The nondetection spell grants a similar benefit to the Amulet:

The target can't be targeted by any divination magic

So JC's ruling should apply to the Amulet as well. This means that divination spells like true seeing will not enable a creature to see you, even if they don't explicitly "target" you.

Senses and abilities not based on divination magic function normally

As the other answers have covered adequately, the Amulet offers no protection against senses and abilities that are not based on divination magic. This includes the Robe of Eyes, unless your DM rules that this magic item is divination-based, which would not be unreasonable. It also includes creatures with a natural ability to see invisible things.

¹ Note: JC's Tweets are no longer considered official rulings. I can't find this particular ruling in the Sage Advice Compendium, so it can be considered semi-official at best, hence the parenthetical qualifier in the heading.