Can anyone identify this or provide a part number by which it can be ordered?
Welcome to Digi-Key’s TechForum. Can you measure the pitch of that connector and let us know what that measurement is? The pitch is the distance from the center of one position to the center of the next position. That will help to narrow down some options.
Looks like 2mm pitch using calipers (18mm between outer pins of a 10-pin connector)
The 10-pin connector has outside body dimensions of 20,6mm x 3,86mm (the solid part containing the pins excluding the retaining clip) and the connector “depth” = 7,83mm