Sounds like a borrowed neutral, in real terms it is a borrowed line (both line and neutral are called live) but this is likely a second fault and nothing to do with the flickering and tripping, although it may give some pointers.
Today two way lights use three wires between the two switches, on is always line, years ago to be able to use twin and earth instead of three core and earth, it was common practice to borrow the line from another light switch, but since it could effect hearing aids giving a mains hum on them, the practice was discontinued.
There was nothing wrong with the practice, in that it did not break the regulations, when both light switches were supplied from the same fuse, however in the 80's there was a move to using two inch spot lights so room was part heated by the lights, this lifted the power used to over 5 amp, so there was a practice to split up and down stairs lighting circuits, this should have included renewing the two way switching cable, but often it was not done, so there are 4 combinations of two way switching, two result in lights off, one lights powered from down stairs and other powered from upstairs, this has never been permitted, but often happens.
The delay has me scratching my head, would seem some thing is heating up, in the old days I would look at the fluorescent lamp, as being the only light with components in likely to be affected by heat, but with compact fluorescent lamps (CFL) and LED lamps there are components in every bulb, seems likely one bulb is causing the problem.
However putting in fuse wire is a time consuming job, I fitted these
https://www.tlc-direct.co.uk/Products/WYB6.html another advert here
https://www.screwfix.com/p/wylex-6a-sp- ... -mcb/48030 they are double the price of the normal MCB but if they will fit in your fuse box, it would make life a little easier, personally I swapped whole box. I also have RCD protection now, but I realise these are unusual times.
As an electrician I do have meters able to help, but they are no magic cure, and if a wire has been damaged by a rodent touching the cable could result in a nasty shock, this is where I would be wearing gloves, but it is so easy when cables are damaged to end up touching a live wire, and with no RCD protection that could be fatal, so I am not happy at the thoughts of you hunting for the fault.
Intermittent faults are the worse you can get, but I would want to eliminate bulbs, so if you remove all bulbs, does the fuse still blow, if not, can you use those bulbs in another circuit and do they work OK in another circuit.
Normally I would say don't play, get an electrician in, but I understand not normal times.