Green’s Dictionary of Slang

agate n.

[the carving of tiny figures into SE agate, a semi-precious stone]

1. a very small person.

[UK]Shakespeare Henry IV Pt 2 I ii: I was never mann’d with an agate till now, but I will set you neither in gold nor silver, but in vile apparel, and send you back again to your master, for jewel.
[UK]R. Nares Gloss. (1888) I 12: agate. used metaphorically for a very diminutive person, in allusion to the small figures cut in agate for rings.

2. (US) a small penis.

[US]Trimble 5000 Adult Sex Words and Phrases 12: agate (Sl.) n. a Penis of diminutive size.
[US]R.O. Scott Gay Sl. Dict. [Internet].

3. see glassy (alley), the n.

SE in slang uses

In phrases

shoot the agate (v.) [the extension of the thumb when playing marbles; note nonce sense by Trimble, in 5000 Adult Sex Words & Phrases (1966): ‘shooting the agate [...] Looking for a chance love partner by walking along with hands at the sides and thumbs extended. In hipster code, this means that a man is asking for sexual companionship, and if a hip female is interested, she may respond without a word being spoken’]

(US black) to walk jauntily with one’s thumbs extended.

[US]A. Lomax Mister Jelly Roll (1952) 19: You should have seen one of those sports [...] walking along with a very mosey walk they had adopted from the river, called shooting the agate. When you shoot the agate, your hands is at your sides with your index finger stuck out and you kind of struts with it.
Record Changer June 10: He would walk with a cake walkish strut and ‘drive them chicks wild.’ This was called ‘shootin’ the agate.’.