Every turns counter I've seen and used are sealed units without a way to illuminate the numbers.
This would be a cool modification to the unit. When I build my 40m transceiver which uses an LCD readout that is difficult to read from more than 2ft., I decided to use outboard LED lighting.
I fashioned a "roof overhang" which I mounted on the outside of the front panel over the LCD readout. The underside of the "overhang" was painted white and I used a strip of 3 ultra-bright LEDS, which has adhesive on the back side, under this "overhang." Since the "overhang" is angled down, the LEDs shine on the LCD readout which now can be seen at any reasonable distance.
I fastened the "overhang" to the front panel with double-sided tape and the only modification to the front panel is a small hole for the 12vdc leads to the LEDs.
Something for you to consider.