Just thought I share my experience regarding Toyota tomtom tns400 this is unit attached to eclipse stereo in toyota yaris and aygo too I think.
The battery of the unit just has N2 and 800mah on it and has a white plug with three wires, Red, Yellow and Black. I measured the battery and the dimensions are: 50mm x 35mm X 4mm.
I searched the internet and auction and websites did not show a suitable item with those dimensions that also had the white plug.

The closest match was: Battery for GPS, Navigator TomTom One 3rd (800 mAh, 3.7 V) with the dimensions 44.3mm x 34.1mm x 5mm.
Took a chance and ordered a battery from a website for 9 pounds, website seemed it was in UK but it was in Netherlands and took longer than a week. I thought the 1mm would not make much difference but it does, the battery is thick but still managed to shut the unit but its not as neat.

I came across a listing without the brackets titled (Battery Replacement for TomTom Route XL, One XXL 540, XXL 550, XXL IQ Routes) and on the page it shows thickens to be 4mm but when I searched online and checked other listing its different and also the plug is different too.

To open the unit used a plastic opening tool you just slide it across the front bezel and there are two clips on each side, then you will see T8 star screws. You have to be very careful as the unit is old and brittle plastic. All four screw nut retainers on my unit broke. Thanks to the clips on bezel still holding together.

The unit connects to the stereo and its always available when driving, you don't have to attach anything to dash or screen. The camera warnings and directions come through the speakers its handy.

Hope this helps, I know many of you must have moved on to better but I cant seem to get on with g/maps when I have selected avoid motorways it still takes me on those routes . May our hobbies stay alive.