From Green’s Dictionary of Slang:
like white on rice (also like gravy on rice) [rice is white itself]
(US black/P.R.) very closely.
1935 [US] Z.N. Hurston Mules and Men (1995) 145: She better not vary, do Ah’ll be all over her jus’ lak gravy over rice.
1938 [US] ‘Sl. among Nebraska Negroes’ in AS XIII:4 Dec. 317/2: Last may be noted some picturesque similes: [...] stick like white on rice.
1944 [US] C. Himes ‘A Penny for Your Thoughts’ in Coll. Stories (1990) 58: They were on him like white on rice.
The Hurston quotation is the only citation for gravy over rice. I wouldn’t include it here; the metaphor is entirely different.