You can actually create an account, pay for one month, then pause it.

Then just unpause in the starlink app to instantly have access and resume billing

This is what I do. I carry the dish in the equivalent of a pelican case [1], and only activate for months I have no other option.

[1] https://www.caseman.com/product/starlink-mount-case/

Can you sign up using Starlink itself? It would by annoying if you needed another ISP when your ISP is down.

Yes, if you just turn on the dish with no account there's still limited "internet" access that lets you access Starlink billing services.

Yes

Paying for a full month if your main ISP is down for a day or two sounds quite expensive. How long does it take to activate?

I used a friend's when I went to see the eclipse in Texas. Didn't time how long it took to activate service on their end because it takes a few minutes for starlink to connect/boot up in the first place and when you're out camping there's other things going on. Less than 30 mins so all I can say. Also, it was $150 for the month.