Jog away; jog off; jog on. Get away; be off; keep moving. Shakespeare uses the word shog in the same sens—as, “Will you shog off?” (Henry V., ii. 1); and again in the same play, “Shall we shog?” (ii. 3). Beaumont and Fletcher use the same expression in The Coxcomb—“Come, prithee, let us shog off?” and again, in Pasquill and Katharine—“Thus it shogges” [goes]. In the Morte d' Arthur we have another variety—“He shokkes in sharpely” [rushes in]. The words seem to be connected with the Dutch schokken, to jolt, and the Anglo-Saxon scacan, to depart, to flee.
Jog on a little faster, prithee, I'll take a nap and then be wi'thee.
To jog his memory, or Give his memory a jog. To remind one of something apparently forgotten. Jog is to shake or stir up. (Welsh, gogi, to shake; French, choquer; our shock, shake, etc.)
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894