My Elddis Typhoon single axle was susceptable to snaking and not only downhill!
It was especially prone to winds on either rear quarter.
Tyre pressures-noseweight and loading helped-especially keeping heavy stuff out of the back end.
Towing up and down the A9 it was subjected to some pretty high winds but of course crosswinds are not restricted to up here eg crossing the border on the west coast M6 A74M.
Hi ancell. Single axle instability and unpredictable behaviour often but not always caused by other vehicles,that was my main motive for only towing twin-axle caravans and large boxed trailers for the last 30+yrs.
Twin axle trailers/caravans have four points of friction down on the ground and that alone contributes to far greater stability than with just the two of a single axle.
This is never more evident than when reversing and maneuvering a twin axle on tarmacadam surfaces,the effort to turn is seen in the distortion that takes place at the walls of the tyres and if the rims are suffering any corrosion and the tyres are running under their correct/appropriate pressure they can/will spill the air from the tyres making for an even more precarious situation.