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You need a variable to keep track of whether the servo is okToSweep and that gets set to true or false at the appropriate time.
In the servoSweep() function you can check that variable - something like this
void servoSweep() {
if (okToSweep == false) {
return; // i.e. do nothing
}
// rest of the code
}
You can use the code from one of the LED functions, with changed times obviously, to change the value in okToSweep.
...R