No one knows Jack of All Trades, really.
The original rules were pretty vague if not unbalancing if handled wrong. One level of Jack of All Trades gave you Level-0 skill in all the others. Wow. That's pretty overwhelming if you think of all the skills with hefty unskilled use penalties. Additional levels in Jack did ... nothing more. Furthermore we are told despite the skill level of Jack involved the benefits were never to equal benefit of having one skill level in the actual skill.
I'm going to try to give you some ways to use Jack that I worked up. As usual pick one you like or make up something you like more. It isn't like I get paid for this.
The easiest way to handle Jack is to allow it to modify the penalty for unskilled use. For example Forward Observer has -4 penalty for unskilled use. A character with Jack-3 would only have a penalty of -1 when acting as a Forward Observer.
Each level of Jack gives a +1 that can be used once per session. Jack-2 gives you a +1 you can use in two instances that night, in whatever skill roll you need to make. It is for 'all trades' after all.
Some situations may be very unusual and require insight and experience as opposed to rote learning and procedure. The classic adventure ANNIC NOVA, for example, dealt with a (very) nonstandard starship. Engineering, piloting and mechanic skills might operate at a minus until the characters get to know the vessel. Jack can reduce these penalties.
The sensors are showing an anomaly. The computer code has an embedded message in it. The alien artifacts can be combined but how. Jack gives you modifiers to the questions that move the story forward. Sometimes that feels better than a +4 to hit.
Characters already have skill-0 with weapons (with some exceptions in COTI). Characters with Jack either have skill-0 with weapons they wouldn't be allowed (doctors, barbarians etc.). If they already have skill-0 or more with a weapon Jack will modify Dexterity or Strength by one point per level when considering required dexterity or strength. For example a Diplomat with no weapon skill but Jack of All Trades -1 picks up a rifle. He uses it at no penalty (that peace talk was really going wrong.) Another character, a Scout with skill-0 and Jack-1 also grabs a rifle. He has Dex 5 but the Jack skill level modifies it to 6 for purposes of using the rifle. He has no minus to his shots. Another Scout with Rifle-1, Jack-1 and Dex 5 grabs a rifle. He too has required Dexterity thanks to his level in Jack and can use his skill 9n Rifle normally (+1 to hit).
A final and probably scary thought. Classic Traveller is sometimes faulted for its minimal experience increases. Increasing and maintaining skill levels is actually very difficult in the real world and Traveller might be more realistic than most games in this regard. I think it follows the tropes of the pulp fiction Traveller used for so much of its inspiration. Pulp fiction had static characters. In any case in Traveller characters acquire the means to be more effective in situations: credits, equipment, artifacts etc. But surely experience is an important factor and while skill levels may not change appreciably a character will surely be able to apply those skills in many new ways. Perhaps instead of more concrete skill levels a referee might award a level of Jack of All Trades to players at the end of a (long) successful adventure.