Green’s Dictionary of Slang

mim adj.

In phrases

as mim as old Betty Martin at a funeral [dial. mim, affectedly modest, demure, primly silent or quiet; the term is imitative of pursed lips. Whether this is the same Betty Martin as all my eye and Betty Martin phr. is unknown]

walking in a prim, orderly manner.

1821–6

‘Bill Truck’ Man o’ War’s Man (1843) 135: Walk, one after the other, as mim and orderly as old Betty Martin at a funeral.