You rode from home and no car or train journey involved? To eliminate the obvious.
Yes started and finished at home, eTrex had all previous track and trip data wiped before i set out.
Yes, but if it hasn't had a GPS fix in the new location yet, the old location will be in the buffer when it starts recording data, and you get a long crow-flies jump at the start. Annoying, but easy to work around when you're aware of it.
OTOH, if "fully on" means you waited for a fix before resetting, maybe it's something else...
I suggest plotting the track on a map in your analysis tool of choice. The nature of the glitch may be obvious. If it's not the first point bug, then my bet would be random wandering due to marginal signal at some point during the ride, possibly in a way that can be explained by the location where it happened (under a roof, urban canyon, proximity to power lines, radar, etc).