electro-luminescent light

I have a oregon scientific Lucca weather display which has a press button to light the display for 5 seconds it also doubles as a snooze button.

The thing I wanted was how to keep the blacklight on without turning off in 5 seconds?

Ask the Manufacturer's technical support; it may have a jumper to accomplish what you want.
If not, you need the schematic or skills to discern the microcontroller pin that enables or supplies power for the light; measure the voltage when on and reroute the lamp lead to a power supply node with the same voltage. The life of the lamp will be shortened if it is EL type.
Miguel