How do I save for an emergency fund if my income keeps changing?

I think you should take such articles with a grain of salt. The purpose of people tagging emergency fund with income is for convenience. The purpose of an emergency fund is, as the name implies, for emergency.

Eg. What happens if you get Covid? Or get involved with a car crash.

You need to decide how much is required. A good rule of thumb is - x months of your income.

Articles are written by people. Different people different approach, choose the advice that best suit your style​​​

Use your expenses as a gauge of your emergency income.

In fact, if your income goes up consistently, thats a good problem.

You should look instead into how you could maybe reduce taxes on your income rather than building more emergency funds. Eg. Topping up cash into your CPF SA account could give you up to $7k relief.

Alternatively, you may consider saving or investing it for future goals.

There is no rule saying that your expenses should increase when your income does!

Yes I agree with you that it should be based on your spending not income. Your spending should nvr increase proportionally to your income, or you'll nvr amass wealth.

Your emergency fund should cover at least 6 months’ worth of expenses. To determine this amount, add up how much you spend in a single month on things that you can’t go without (e.g. food), and the contributions you owe each month (e.g. monthly savings or a mortgage).

Remember that if you were to lose your entire monthly income, your savings goals shouldn’t be compromised-- they’re there to make sure you reach your long-term life goals! Don’t let an emergency get in the way of that.