What might be wrong with mains wiring that behaves as follows, connecting
two lamps in parallel to two switches, S1 and S2.

When S1 is switched one way, everything works fine: S2 toggles the lamps on
and off.

When S1 is switched the other way, the lamps are always on.

Now swap L1 and L2 inside S2, and we get

When S2 is switched one way: everything works fine: S1 toggles the lamps on
and off.

When S2 switched the other way: lamps always on.

Thanks for any help with this.

There is no fault in either switch.