Where does “stopcock” come from?

I can't write this etymology sentence because the chain provided appears corrupted or nonsensical—it cycles repeatedly through "English ten" and "English cocking" without progressing to older languages or establishing a coherent etymological pathway. A valid chain requires distinct steps moving backward through actual language ancestry. Could you provide the correct etymological chain?

stopcock (English): A valve, tap or faucet which regulates the flow...

Definitions

  1. A valve, tap or faucet which regulates the flow...

Ancestry of “stopcock”, step by step

stopcock traces back through two separate lines of ancestry.

via English cock

StepLanguageWordMeaning
1EnglishcockA male bird, "especially:"; A valve or tap for...
2Middle Englishcokrooster, cock; rooster crest, comb; heraldic...
3Old Englishcōca cook
4Vulgar Latincocus
5LatincoquusA cook; person who makes food
6Latincoquōto cook; prepare food
7EnglishCookA placename
8Germankochento cook, to prepare food; to boil; to be stirred...
9Middle High Germankochento cook
10Old High Germankohhōnto cook
11Proto-Germanickukōnąto cook
12Latincoqueresecond-person singular future passive indicative...
13Proto-Italickʷekʷōto cook
14Proto-Indo-Europeanpékʷetito be cooking; to ripen
15Proto-Indo-Europeanpekʷ-to cook; to ripen
16Proto-Indo-Europeanh₃-ép-kʷ-

via English stop

StepLanguageWordMeaning
1EnglishstopTo cease moving; To not continue; To cause to...
2EnglishtopThe highest or uppermost part of something; A...
3Middle EnglishtopThe summit or top of something, especially a...
4Old Englishtopptop, summit (of something)
5Proto-West Germanic*topptop, summit, crest
6Proto-Germanictuppaztuft, plait; top, summit
7Proto-Indo-Europeandumb-tail, rod, staff, pole, penis; tail, rod, staff,...
Every word from Proto-Indo-European h₃-ép-kʷ-Every word from Proto-Indo-European pekʷ-Every word from Proto-Indo-European pékʷeti