The first and foremost reason for this post is I am looking for interesting ideas for materials, and ingredients to augment a previously magical weapon.

The augmentation I have in mind would be to turn a +1 weapon into a Weapon of Warning.  Some ideas that are rolling around in my head are along the lines of "The unblinking eye of a powerful undead", thinking any above CR 2 or so, something thematic for hearing, and something along the lines of tremorsense based or something else along those lines.

Ankheg antennae, eyes or legs of a Cave Fisher, beak of a Grell, Twig Blight hearts, lots of possibilities for creatures with those traits.  What I am having more trouble with is maybe some other natural options.  Along the lines of herbs or rares stones that might be properly thematic for watching, warding, guarding, alertness.

Bellflower, bluebell, or other plants with bell in the name. Foxglove and fuschia and angels trumpet, among others also have bell shaped blooms. Now that I’m thinking of it, you could include some kind of special bell, forged by some special person or group as a component. 

I googled protection stones, and there’s a long list on some of the new age websites. Skimming them most are pretty specific, but for general protection, obsidian might work, or fire agate. 

I don’t know how rare any of them are, but if you’re the DM, you can make them as rare as you like. Or just say, sure foxglove grows everywhere, but only the foxglove from the shadow of mount doom will do the trick for this. 

I did a web search and a reddit link took me to the Monster Harvesters Handbook

There's also a three volume series called Monster Loot on DMSguild.com

You might also consider researching what certain plants, minerals, and chemicals do in real life and interpret that into your possible crafting materials. Although not applicable to your specific needs, pitcher plants, venus fly traps, bladderwort, and sundew are all carnivorous plants that feed on insects. These could be used to create an "insect-bane" weapon or Finn's grass sword, just as an example. There are no natural ingredients that come to mind that literally provide a real-life "warning" when used, I can only think of technological advances, but if something exists hopefully it wouldn't be too hard to find.

Edit: "Canary in a coal mine" would be fun to interpret into a crafting ingredient.

Material Spell Components in 5E could be useful.  The author made available a spreadsheet of all the components used in 5E spells.

Oddly enough, there are several sources on harvesting monster parts, and what those parts are worth (idea being they are used as spell components).  Unfortunately, there's basically nothing about how to go about using those parts.  Most magical item creation "how to" guides are just expanded versions of the DMG:  Throw lots of gold at it over lots of time and it magically becomes magical.

Hmm maybe something like a Cat's Eye gem and and some coffee or tea of some special variety or circumstance?  Like coffee grounds from a watchtower, or tea leaves from the land of Chult type deal?

You could go for metaphorical ingredients, like the voice of a spider or the watchfulness of an elk.

Make them find something that they think will work...  Something to bear in mind.

An item of oracular nature, the party has something that fits this with the gold sun elf statuette from lost mine of phandelvar.  Other items could be like a dowsing rod, bones used for divination and others in that vein.

An ever watchful eye, a tigers eye stone, or eyes of a decent strength undead, perhaps a rare plant named after an eye would also fit the bill.

I am stumped on third part I wanted to add, or rather the wording for it.  Trying to leave it slightly open ended for the players to decide what they think the appropriate item would be.  I am thinking along the lines of something to do with vibrations.  Ankheg feelers, tuning fork, plants that react when they feel vibrations, those kinds of things.  Any suggestions for how to communicate that particular idea simply to the players.