How to get medical insurance for a Singapore layover?

I am travelling to Australia from Europe, with a layover in Singapore on both legs of my travel. On my outbound trip, I have a 15-hour layover and I will surely visit the city; on the return, I have ca. 6 hours and I may decide not to leave the airport.
I am worried about medical assistance in case of emergencies during these two layovers (during my stay in Australia I am covered by a reciprocity agreement between my homeland and Australia).
I find various insurance options about travel medical assistance, but they insist on covering the whole trip and not just an isolated day or two which are a small part of it. So, my questions are:
Am I going to need a medical insurance for a layover in Singapore? Even if I don't leave the airport? Or are medical emergencies covered for free by the state health services?
If the answer is yes, where can I buy medical insurance for such a short period of time? Directly through a Singapore company? Or maybe is there a company selling travel assistance in Europe that is flexible enough to cover only a short part of a trip?
Best Answer
If you're unprepared to buy for the duration of your trip (which may still be wise, if there are restrictions on the reciprocity between Australia and your homeland), the easiest option may be to get a credit card that provides travel medical coverage. This will generally cover trips up to a certain duration, so the length of your trip will matter. The cards usually include other benefits that are useful to travelers too, such as baggage coverage.
Even if you could buy the short-term coverage, there would be a minimum premium for each burst of time you need it, so you might pay as much for a single day as you would pay for a week or two of coverage; it may not be as cost-ineffective to insure the whole trip as you think.
Bear in mind, too, that if your aircraft stops in another country because of your medical emergency, it is possible you could end up in another country than these completely unplanned, as well, and need medical insurance there, too. This is also possible if your aircraft stops for mechanical issues or for any other reason.
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