In an answer to the recent question, What is the American equivalent of a "backie"? site participant Chappo notes that in Australia the word dink is sometimes used as a noun to mean "a lift on a bicycle" and the verb dink can mean "carry a person on a bicycle" (both definitions provided by Oxford Living Dictionaries online). OLD has this very brief source note:
Origin 1930s: origin unknown.
A term familiar in Australian English but not widely used most other parts of the English-speaking world is dinkum. G.A. Wilkes, A Dictionary of Australian Colloquialisms (1978) gives two entries for dinkum:
dinkum n. 1 Work, toil: obs. {E. dial. OED 1891} [Citation from 1882 omitted.] 2 An Australian soldier in World War I: obs. [Citations from 1918 and 1919 omitted.]
dinkum a. & adv. authentic, genuine, esp. in the expression 'fair dinkum' ('on the level') [Citations from 1894–1973 omitted.]
Jonathon Green, Cassell's Dictionary of Slang, second edition (2005), lists several meanings for dinkum in Australian slang (to much the same effect as Wilkes's definitions above) and three relevant meanings of dink in Australian slang:
dink n.5 {1930s+} (Aus. juv.) a lift on the crossbar of a bicycle (cf. BUNK v.5). {ety. unknown}
...
dink adj. 1 {1900s–1930s} (Aus.) honest, genuine, trustworthy. {abbr. DINKUM adj.}
...
dink v. (also double-dink) {1940s+} (Aus. juv.) to give anyone a lift on the crossbar of one's bicycle (cf. BUNK v.5 {DINK n.5}
The entry for the verb bunk cited twice in the definitions above identifies it as a 1950s Australian slang term meaning "to carry someone on one's bicycle crossbar" and later a 1980s+ term meaning ""to travel without a fare, to get in (e.g. to a cinema) without a ticket."
My question is this:
What evidence (if any) is there of a possible etymological link between dink (the bicycle ride) and the earlier dinkum (either in the adjective sense of "authentic or genuine" or in the noun sense of "work, toil")?