I've seen a lot of players contemplate luck, but ultimately decide that it isn't worth the points. I had a thought for a limited version, simultaneously more and less powerful.
Fortune: Reroll a single die of a roll, once per roll, 2 pts/lvl, maximum of 5 levels.
This puts it similar to systems including a luck stat, such as the Edge from Shadowrun, giving you either rerolls or extra dice (functionally very similar, as it's a Total Successes system).
It's 1/3 the power of luck (reroll 1 dice instead of 3), but gives you a bit more fine ability to influence things. I've seen many a player die or nearly die in GURPS on a single dice on things like dodge rolls. Roll a 6, 1, 1 when trying to get below 7. A single die lost it for them. Meanwhile, Fortune can't turn a crit fail into anything better than a 12 or 13. You are likely at best to get away with changing a critical failure into a regular failure, maybe squeeking by with a success if you manage to reroll into a 1 and are substantially skilled. A full luck roll will likely get you approximately 10, due to the bell curve of 3d6, whatever you started with. But, this greater finesse gives the player a harder decision of when to use it. Do they save it to get out of a crit? To turn a failure by 1 into a just-barely-success? Reroll a 1 on a damage roll in hopes of ending the fight before they need to reroll something else to survive?
Took another look at the rules for Luck. 1/3 cost for 1/3 power made sense when I was thinking luck was once per session, a single reroll. Upon double checking, it gives you 2 rerolls, once per hour of play. I think I like the functionality of Fortune as listed, but it's cost has been reduced and more uses per day are permitted.