I am not very fond of the way Wealth, Status, Jobs, Cost of Living, and the like interact in GURPS, as it manages to combine being not very realistic, not very well balanced, and a bookkeeping pain. This particular variant is pretty explicitly gamist, rather than simulationist, but it doesn't do a horrible job as a simulation -- it's just not designed for that.
Ignoring realism for the moment, there are two basic ways we can come up with a value for income:
We come up with a disadvantage value for 'works X days per month', and assign an equal amount of Independent Income.
We just assume that working is training, and 200 hours gets you 1 point in money.
For the first method, our equivalents are Extra Sleep and Slow Eater. Both of those are roughly [-2] for 1 hour per day, or 30 hours per month. However, this differs meaningfully from working in two ways: working counts against the hours you can spend on Long Tasks (B346), and time spent working counts towards Learning on the Job (B293). It also might involve time spent commuting, or it might require you to be available, which can significantly interfere with adventuring (in effect, it's a non-hazardous duty). In any case, this argues for at least 0.5% per day, and possibly somewhat more.
On the second method, our equivalents are Trading Points for Money (B26) and Signature Gear (B85). This argues for 0.4% per work day (25 days = 200 hours), or even 0.3% (because of Learning on the Job). On the other hand, Trading Points for Money is inordinately inefficient (10 points double starting wealth. 10 points in Wealth doubles starting wealth, but also increases earning ability and might push you over a breakpoint for Status).
Overall, I find myself liking a rate of 0.1% per hour, meaning a full-time job (20 days/month) is worth 16% per month.
This box has two major changes:
Starting wealth is only for adventuring gear and liquid wealth. Settled characters may choose to buy background wealth (below).
Trading points for money gives 20% (not 10%), and is affected by wealth level; this is always available for adventuring gear. You may, if you wish, take up to -4 points in reduced starting cash (a character with -4 starting cash and +4 background wealth is a reasonable settled character).
Background Wealth (var)
A character may declare they have background, non-adventuring wealth. Treat this as as potential advantage (B33); you get the wealth, but only for non-adventuring purposes, and can upgrade it to adventuring-usable as normal.
Status and Rank, as given in GURPS, no longer exist. They are replaced by two concepts:
Influence (var): influence is a measure of temporal power; it describes the amount of resources you control (as opposed to what you own). Characters have a base influence equal to their wealth (as they always control their own resources). To have additional influence, simply buy extra wealth with a limitation that it's associated with your position, rather than your person, and must be used in a way appropriate to that position (how limiting this is varies extensively). Thus, while the actual wages of the president are modest (roughly Wealthy), the resources controlled by the office are equivalent to something like 175-200 points in wealth (200B-2T in adventuring gear -- basically, the US military). Influence does not directly give a reaction bonus, except as people think that you might spend that influence in a way that's beneficial or detrimental to their goals. Influence includes the wealth/influence of people who are expected to spend it (and if you have superiors, the possibility they will require you to act in ways you don't want to is part of the limitation on Influence).
Social Regard (5/level): this is a generic reaction bonus.
The key thing about both of these concepts from a gamist (rather than simulationist) perspective is that they don't matter. The number we actually care about is the amount of leftover money you have
A basic change to the system is that trading points for money gives 20% (not 10%) and is affected by your wealth level. The change to 20% is because otherwise it isn't sensibly competitive with actual wealth