Where does “toothpick” come from?

I need to stop and note that the chain provided doesn't support an etymology for "toothpick" — it only contains variants of "pick," "peep," "pip," and "pippin" with no clear connection to toothpicks or their origin. I cannot write an accurate origin summary because: 1. The chain doesn't explain how these elements combine to form "toothpick" 2. No oldest language or original meaning is provided that would justify this etymology 3. Following the rule "state only what the chain supports," I would be inventing the connection Could you provide the correct etymological chain for "toothpick"? A typical chain might trace it through its component parts (tooth + pick) to their respective origins.

toothpick (English): A small, usually wooden, stick, often pointed at...

Definitions

  1. A small, usually wooden, stick, often pointed at...

Ancestry of “toothpick”, step by step

toothpick traces back through two separate lines of ancestry.

via English pick

StepLanguageWordMeaning
1EnglishpickA tool used for digging; a pickaxe; A tool for...
2Middle EnglishpikenTo pick at; to use a edged tool on; To pierce or...
3Middle EnglishpykeA sharp round point or projection; A point or end...
4Old Englishpīcpointed object, pick axe
5Proto-Germanic*pīk
6Latinpixpitch, tar
7Proto-Indo-Europeanpik-to be angry; pitch; resin
8Proto-Indo-Europeanpi-sap, juice

via English tooth

StepLanguageWordMeaning
1EnglishtoothA hard, calcareous structure present in the mouth...
2Middle EnglishtothAlternative form of tothe
3Old Englishtōþtooth
4Proto-Germanictanþstooth
5Proto-Indo-Europeanh₃dóntstooth
6Proto-Indo-Europeanh₁ed-to eat

Words derived from “toothpick

Every word from Proto-Indo-European pi-