Well that was pretty cool. After writing my above response the forum advised me that someone had already responded to the thread and I may wish to revise my response. Pretty cool.
Okay, here is what I found on Google relative to the history of the term "Jumping the gun":
"Comment from Philip Page: In military use, used by the Royal Artillery from years ago to describe poor timing by the infantry and later armour with regard to advancement or attack into area with preparatory artillery barrages. With the earlier smoothbore cannons, infantry was commonly slightly behind batteries, to advance as the enemy closed to prevent loss of guns. Some ill-disciplined troops would literally jump the guns to have a bash at the enemy.
Definitions from Steve Sabram: 1) Refers to track and field events where everyone is to run after a starter's gun is fired. If you started to run before it was fired, you "jumped the gun". 2) Referring to the Oklahoma Land Grab of the 1800's. All of the settlers literally were at the territory border 'til a cannon was fired allowing them to move into the territory to make a claim. If you ran before the cannon was fired, you were shot by US Troops. Thus "jumped the gun"."