Не знаю, на мой взгляд «танец» - это «тянуть», «тянуться». Собственно и Вы об этом же. Даже лучше – тянец.
Очень неосознанно, но британцы подтверждают эту этимологию.
dance (v.)
c.1300, from Old French dancier (12c., Modern French danser), of unknown origin, perhaps from Low Frankish *dintjan and akin to Old Frisian dintje "tremble, quiver." A word of uncertain origin but which, through French influence in arts and society, has become the primary word for this activity from Spain to Russia (e.g. Italian danzare, Spanish danzar, Rumanian dansa, Swedish dansa, German tanzen).
In part the loanword from French is used mainly with reference to fashionable dancing while the older native word persists in use with reference to folk-dancing, as definitively Russ. pljasat' vs. tancovat' .
Replaced Old English sealtian, itself a borrowing from Latin saltare "to dance," frequentative of salire "to leap" (see salient; "dance" words frequently are derived from words meaning "jump, leap"). Related: Danced; dancing.
It is strange, and will, I am sure, appear to my readers almost incredible, that as far as I have ever read, there is no reference that can be identified as containing a clear allusion to dancing in any of our really ancient MS. books.
Как Вам староанглийское «sealtian» и лат. «saltare»? Кстати, вон и «паяц» выполз, от русского «плясать».

salient (adj.)
1560s, "leaping," a heraldic term, from Latin salientem (nominative saliens), prp. of salire "to leap," from PIE root *sel- "to jump" (cf. Greek hallesthai "to leap," Middle Irish saltraim "I trample," and probably Sanskrit ucchalati "rises quickly").

А, «leap»? Прямым текстом – «лупить»! Такое случается в жгучих танцах. Особенно умиляет «греческое» хлестай.

А слово «танк» - это «чан». Вероятно и чарка. И «чокаться».
И британцы с этим согласны:
tank (n.)
1610s, "pool or lake for irrigation or drinking water," a word originally brought by the Portuguese from India, ultimately from Gujarati tankh "cistern, underground reservoir for water," Marathi tanken, or tanka "reservoir of water, tank."

Perhaps from Sanskrit tadaga-m "pond, lake pool," and reinforced in later sense of "large artificial container for liquid" (1680s) by Portuguese tanque "reservoir," from estancar "hold back a current of water," from Vulgar Latin *stanticare (see stanch). But others say the Portuguese word is the source of the Indian ones.

Meaning "fuel container" is recorded from 1902. Military use originated 1915, partly as a code word, partly because they looked like benzene tanks. They were first used in action at Pozieres ridge, on the Western Front, Sept. 15, 1916. Slang meaning "detention cell" is from 1912.
Правда, очень хитро вывернули – занесено португальцами из Индии, будто зараза какая. Кстати, и «канистра» (canister) отсюда же. Переход «ч» - «ch» - «с» (лат.).

Да, тянуть и сталкиваться – видимо из одного куста. Стакнуться - сговориться. Не зря «take».
Тяг (нути) – толк (ать). Сюда же и «толковать» (talk).
Словарь 1675:
TO DANCE (dantzen, Teut. dancer, F.) to actuate the Body according to composed Measure
Вот и пословицу подогнали. Почувствуйте сексуальную подоплеку:
“NO LONGER PIPE, NO LONGER DANCE”
Мой вольный перевод: « мы без длинного «уя» не танцуем ни «уя». Простите за графоманство.
This Proverb is a Reflection upon the mercenary and ungrateful Tempers of too many People; and is also a good Memento of Prudence, intimating that Misfortune will have few or no Friends; for ungrateful and mercenary People, though they have had twenty good Turns done formerly, will danceno longer that while the Musick of this Proverb obliges them for their Pains; nor budge no further than they have Money to pay them for their continued Service.
Собственно, объяснение об этом.
А, вот дальше – еще интересней
DANCETTE, DANCY – (in Heraldry) is when the Outline of any Border is largely indented (примерно так – в геральдике внешние линии (линии краев) существенно отступают (от края чего-либо, надо полагать, например в гербе или на знамени). То есть – оттянуты от края.
Кстати, «тон» в музыке, вероятно от «тянуть».
Впрочем, как и «язык» - «tongue»
И «тонна».