Green’s Dictionary of Slang

home sweet home n.2

[rhy. sl.]

a comb.

[UK]Western Dly Press 12 Jan. 2/3: Other popular rhyming slang terms are [...] ‘Home sweet Home’ (comb).
[Aus]R. Aven-Bray Ridgey-Didge Oz Jack Lang 31: Home Sweet Home Hair Comb.