Green’s Dictionary of Slang

eel n.¹

1. the penis.

c.1608		Shakespeare, Pericles IV ii: Thunder shall not so awake the beds of eels as my giving out her beauty stirs up the lewdly-inclined.
1622		Fletcher Sea-Voyage IV i: Ye had best come search us, A Seaman is seldom without a salt Eele.
1654		Mercurius Fumigosus 29 13–20 Dec. 231: The Ele [...] wriggl’d into the Eele-hole between her leggs.
1732-1820		Order of the Beggar's Benison and Merryland (1892) 64: ‘Haud it fast, my bonnie lass, — it’s a fine big Silver Eel’.
1836		‘Cock Salmon’ in Frisky Vocalist 41: And when her soft bosom he offered to feel, / She pinched him and vow’d she would skin his eel [...] ‘That’s just what I want,’ said fishy, so free, / So pull’d out his eel, as she sat on his knee.
2003		G. Carlin GeorgeCarlin.com 🌐 Condom: eel skin.

2. a very thin person.

1928

R. Fisher Walls Of Jericho 28: ‘Cause you ain’ got none to leave, you doggone eel.

In compounds

eelpot (n.)

the vagina.

1890–1904		Farmer & Henley Sl. and Its Analogues.
1896		Farmer Vocabula Amatoria (1966) 78: Cornet, m. The female pudendum; ‘the eel-pot’.
c.1904		A. Crowley Snowdrops from a Curate’s Garden 25: Alec had his middle finger in Ada’s eel-pot.