JOT is an interesting skill. And, I've seen a lot of uses for it over the years. There's what's written in CT. DGP took a different direction with JOT in their magazine, Travellers Digest. Some 3PP's would take even another direction with the skill.
Here's a couple of ways I have used JOT in the past.
METHOD I: JOT as a point pool for the night's gaming...
First, consider the TACTICS skill. This is something I first saw back-in-the day DGP's Traveller's Digest, then it re-appeared, sort of, in MT, before making another curtain call in T4.
A character's skill level in Tactics is considered a point pool that can be used on any combat task roll during the night's game session. This Tactics pool "re-fills" before the start of the next game session.
So, in effect, a character with Tactics-2 has a +2DM that can be applied to any combat task roll (of the player's choosing) during the game session. Alternatively, the player could split this up, using a +1DM on one combat roll during the night, saving the remaining +1DM for another combat throw later on. I even allow this DM to be applied to Damage throws, increasing damage to an enemy.
Using the skill this way, all of a sudden my players are very, very happy when their characters acquire skill levels in Tactics during character generation.
The Tactics pool can be, if the owner of the Tactics skill agrees, used by other members of the party. This is akin to someone saying, "You brace your weapon on that rock, point in that direction, and let fly with the trigger if anyone comes around that bend!"
If someone, not the owner of the Tactics skill, is trying to use one, some, or all of the points from the Tactics pool, the number of points used is limited by the Leader skill of the character who owns the Tactics skill. If he doesn't have the Leader skill, then he's consider as having it as Leader-0 (a Default skill), and the maxmum points from the Tactics pool that can be transferred this way is 1. Should the owner of the Tactics pool have Leader-2, then two points could be transferred to another character.
Looking at Jack-o-Trades, it can be used the exact same way as Tactics is described above. The only difference is that Tactics is used for combat throws while JOT is used for non-combat skill checks.
METHOD II: My favorite method...
This is one of my favorite ways to play JOT. Once a task was barely missed--just by one point--JOT may allow the player to turn that just-missed failure into a success.
JOT is useless unless the original task is failed by exactly one point (no more). What this simulates is the character relying on his ability to overcome problems and adapt solutions quickly.
Here's an example of how it works: Leonardo is attempting to fix the busted ship's comm. The vessel's captain doesn't feel like getting blown out of the sky because he can't communicate with the idiots manning the traffic control towers at the ship's next port of call.
Leonardo needs a 10+ to fix the ship's comm, but ends up rolling a 9. He fails.
But, since he missed by one point, Leonardo can rely on his JOT skill to (maybe) jury-rig the sucker so that the comm is up an working again--at least for a little while.
Leonardo missed is communications repair roll by 1 point. But, he's got JOT-3.
This task is elligible for a JOT check.
Leonardo rolls 1D for 3-. If successful, Leonardo gets to attempt the exact same commuications repair roll a second time (another chance to fix the comm). If the JOT check fails, then the comm stays busted.
And, if Leonardo feels very risky, he could roll 2D for 3- on his JOT check. If successful, he'll get a +1DM on his second earned comm repair roll.
In short...
JOT is not used at all unless a task is missed by exactly one point. When that occurs, a JOT check is made: Throw 1D for JOT skill level or less. Success means the resourceful character is allowed a single retry at the skill check. Failure means no retry possible.
If the character wants to get a positive modifier on the retry, he simply throws more than 1D. 2D for JOT skill level or less gets the character a +1 DM on the retry throw. 3D for JOT skill level or less get the character a +2 DM, and so on.
Pretty simple.
Incidentally, the Tactics skill could be used in the same manner for combat throws.
But...does the character get a benefit from having JOT-6 or more?
Yip. A character with high JOT skill would have an option. A JOT-6 character could automatically get the retry (if he missed originally by 1 point on the original task), or he could try to get a bonus on the retry (learning from his mistakes...I did this, and that did that, so I did this, and now it does that...).
For every extra D6 rolled on the JOT check, a +1DM is added to the retry throw.
So....
1D for 6- means a retry is allowed.
2D for 6- means a retry is allowed, and a +1DM is used on that retry.
3D for 6- means a retry is allowed, and a +2DM is used on that retry.
...etc.
With a JOT-6, it's up to the player. He has a 100% chance of success on a retry if he goes for the 1D check. That chance is about cut in half if he goes for the 2D check...it's riskier, but the +1DM benefit is the reward for succeeding on a riskier check. For a +2DM, the player would roll 3D for 6-.
METHOD III: DGP's system...
It's been a while since I read it, but, if memory serves, what DGP did was one that I've seen copied a lot and used under various definitions. Basically, there is some system in place that allow the JOT skill level to "soak up" negative modifiers. So, a throw that would normally have a -2 DM associated with it would be reduced to a -1 DM if the character had JOT-1.
I always thought that system was a bit overpowered.