Leveraging DC series circuit to power higher voltage LED panel
Fortunately, the Phidget seems capable of using an external power supply of up to 15V. They say 


Externally Supplied Current Consumption (max) VDC = 15V


It seems you can probably use an external 12V supply and no resistor with the Phidget doing the current control BUT you should talk to a dealer or the user commuinity who MUST have done this before.

Just possibly:

12V, 1.25 W. I = 1.25/12 ~= 0.104A

Use 15V and LEDs are 12V so.
 R = (Vsupply-Vled)/Iled = (15-12)/.104 =~ 29 ohms.
 27 ohm std E12 value probably OK. Use 0.5 Watt or higher.

BUT see dealer or user community.