Green’s Dictionary of Slang

act the (giddy) goat v.

also …silly goat, play the (giddy) goat
[goat n.1 (2); the assumption is that the animal is naturally foolish; note Stephens & O’Brien, Materials for a Dict. of Aus. Slang (ms. 1900–10): ‘No doubt a humorous variation of “caper”.’]

[late 19C+] to behave foolishly.