The status light on the Rechargeable Trackpad T651 isn't meant to stay on. This is the normal behavior of the trackpad.
When you turn on your trackpad, the light will come on for a few seconds. If the light is:
Green — trackpad battery level is good
Red — trackpad battery level is low
After displaying the battery status, the status light indicates the trackpad's Bluetooth connection status:
Blue — trackpad is connected to a Mac
Blue (slow flashing) — trackpad trying to connect to Mac
Blue (rapid flashing) — trackpad is ready to pair via Bluetooth to a Mac
NOTE: To conserve power, the LED will turn off shortly after displaying the battery level and Bluetooth connection status.