Change the transmission fluid, the first rule of sorting autobox problems - it may well sort the issue completely - but if it doesn't, it rules it out as a possibility.

Given the production dates for the 406 it's probably on starship mileage by now.

OK go onto youtube and put in your vehicle and the problem ,there people on there who do this for a living and you can see just whats going on if you dont have the skill set to change the fluid you will have to take it to someone who knows how to do it , these days we have things like level tubes to check the level and the fact that it has to be checked at working temp , then you have things like the level tube is hidden up inside the drain plug hole and you need an 8mm allen key to get it out to drain the unit ,thats if you have a modern unit

so before you decide to do it, check on how to first from people who know how to and whats involved !

I had a Seat automatic and asked a dealer what fluid to put in it he said dextron 111 so drained it and put the dex 111 in it the gearbox had a mind of its own and kept changing down i went onto youtube and found it had to have VW synthetic fluid changed the fluid and the prblem went and the car drove as it should and that was a main Seat dealer, i now have dozens of you tube videos on how to for my car and do the work my self !