Used to turn off a router temporarily whenever a new public IP was needed, which took almost 3 minutes to get back up and running. Then instead of this, unplugged the telephone cable for 5 seconds, which gave a new IP in under a minute.

Then put a mains electricity type switch next to the mouse to physically disconnect the telephone wires (in fact the dual one in the attachment to disconnect both wires single-handedly and while sitting). Which seemed to work fine but after some weeks or months access to the internet became unstable and maybe bandwidth was reduced too (didn't measure it though) and went back to unplugging.

What might be a better physical switch for the sort of signals used with ADSL/VDSL?

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This depends on the router and the ISP. Your router may have a feature to reacquire the IP address, but it depends on the ISP whether you get a different one.

I don't know whether your internet instability is caused by the switch. Perhaps it was switched too often, and a new switch solves the problem? A less flimsy one? The fact that it worked weeks or months is evidence for material fatigue. Or perhaps the instability is unrelated to the switch.

Checked the wires inside carefully back then, didn't see anything flimsy. Must have been something developing on the surface of the contacts. Or the ISP changed/upgraded something. Wouldn't spend any money on an identical switch.

Notice there was no instability when I went back to unplugging and plugging the RJ11 plug.

Maybe this?

https://www.walmart.com/ip/RCA-VH71R...witch/11600137

Is it really coax? RG something on wires? I assume that would work. Might peek at solidsignal for stuff like that too.

What do you mean? What is RG short for?

ADSL/VDSL uses old POTS wiring and trying to get a COAX switch to work would be somewhat futile IMO. VDSL frequencies could be around 22 MHz and a single pole switch should be adequate without significantly "harming" the signal. Physical location near the computer or how you wired the switch could be the reason of the instability. Regular mechanical power switches could develop oxidation but they are rated for much higher current and thousands of operations.

A simple toggle switch should work but the question is how often are you pulling the plug? I'm the lazy type would probably just stick to pulling the RJ11.

RG - Radio Guide is a specification for COAX cable i.e. the typical wire used for cable TV and to connect antennas.