Blinking an LED once when a slide pot is pulled to ~zero ohms
Untangling the schematic a little we get this.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. The OP's schematic redrawn.

Not it's a bit clearer that when the Range Fine pot is reduced towards zero that we should see 5 V appear at 'A'. To get your required output you need to do two things:


Add a voltage comparator at A and arrange it to turn on at 50 mV below the 5 V rail or whatever tolerance you decide. You will need a comparator with rail to rail inputs because you are working right up to the 5 V supply. (Strictly you don't need it to work to 0 V but you're unlikely to find one that goes to V+ and doesn't go to zero.)
Arrange for the comparator output to drive a pulse generator to blink the LED. Since you're comfortable with the 555 it would make sense to use another for this.