How about just buying a new backlight and save the hassle of not ever getting the right answer...
To help you out, older Frequency Counters used in the Galaxy, Uniden and Cobra sets, per what
@nomadradio was making a suggestion to, the IF of each radio a Frequency counter that uses the IF - TRANSLATES that IF into a number, being your Frequency.
Problem is, many radios used a different loop frequency, until just recently - when most are now stabilized to the 10.240 MHz standard although a few outliers like those from President. They made rouge versions of the Cobra 148 GTL - but called it DX.
As you will find out, that counter was pretty versatile.
The counter you are using now, from Galaxy that FC347, is Pre-programmed - it won't work on your Cobra very well. Why? The loop the FC347 uses is based upon a 13MHz Crystal, so it's loop frequency is a DIFFERENCE between the PLL IF loop and its' own loop - with the "base" loop of another set. IT's Galaxy's way of doing things...
So they do offer the FC347 but when you use it in Cobra or Uniden, you'll need to set some jumpers on the board so it knows how to sample, count and calculate properly.
To help if you do your research on the FC347 - yes, IT SHOULD work, but you'd still be better off using the main faceplate unless you've done away with it and want to use a Frequency counter with your Delta Tune as a Slider - well I can't blame you for trying - Good Luck!
You might want to try Para-Dynamics PDC-356 instead.
Wanted to give you a piece of history though, the Para-Dynamics Offered a Frequency Counter that used BCD switch setup to alter the count the Sampler did, for its' calculations - a Rotary BCD switch set of 4 were used in this old fossil ... PDC-256...
PDF Attached...