Speed Twin - Changing Mode By Itself?

It does sound like a voltage supply drop out.
Check around the headstock area for wiring strains and chafing.
Breaking and remaking jackplugs, with a spray of water displacer, GT85 or similar, wouldn't go amiss and may identify a dodgy pin.

The nearside/ left-side of the headstock was a favourite on the gen 1. I removed the left bracket and machined off the sharp corner of the headlight bracket.
Wiring damage

Note original shape of headlight bracket (satin black, bottom left of picture).

Note new shape of headlight bracket


This seemed to resolve it nicely so I removed it again and had it re-powdercoated.

 

Speed Twin is now a confusing term thanks to Triumph changing the names.
Just for clarity, the above pics are from a 2019 StreetTwin 900 (now called Speed Twin)

Hopefully this will give you some idea's to check, irrespective of specific model

 

I had a similar problem with my 2019 Speed twin 1200, when it would reset the trips and clock to zero if I had to crank it over more than once. Although the battery seemed OK when I tested it, a new battery cured the fault and it has never re-occurred since.

 

Mrs Visor has just had an issue with her Sreet Triple. It changed mode by itself and then wouldn't change at all for a while then be able to change once.....you get the picture. Having done a load of research it would seem water ingress is the issue (certainly with hers) and is having to get a new switch assembly on Friday
You would think that Triumph would sort this as it's guaranteed to see water at some point in its lifetime