Green’s Dictionary of Slang

gill n.1

also gil
[ety. unknown]

1. [late 16C–1950s] (also gills) a gullible person.

2. [19C–1910s] (also gillie) a general term for a man.

3. [early 19C] an interfering person.

4. [late 19C] (UK Und.) oneself.

In phrases

his gills (n.) (also her gills, his jills)

[late 19C–1910s] (usu. Aus.) a self-important person, an authority, ‘his nibs’.