as from what I learn from one famous financial adviser here, you should have at least 6 months buffer or emergency fund. Like in case that you lose our job, at least you still have the money to continue to live and pay the bills until you got a new job. So you will not be pressured at all and as you have said, peace of mind knowing that you still have the money to sustained. Worst case is that you can't find a job in that timeframe but I doubt if if you are really resilient to go find a new one. I have know someone, like that, in just a week she finds a new job and so her emergency fund is still intact and then he can continue to pay for the mortgage of her house.
Never knew about this "to have 6 months emergency funds saved upfront" and I will put it into practice.
For me, the emergency funds I like saving up to are what could last for me for a month. I haven't thought about having more emergency funds just in case the unexpected happens, like losing my job.
However, with this info learned, I will begin now to act fast, have more emergency funds so that I will have something to hold on to for some months, even when I have no source of income, my bills will still be paid from my emergency funds untill I bounce back(having a job or business)