Modification of the cylon script from https://learn.adafruit.com/larson-scanner-shades/software that allows the start position on the strip to be specified.

cylon.ino

#include <Adafruit_NeoPixel.h>

#define PIN      1
#define N_LEDS 100
#define START   50

Adafruit_NeoPixel strip = Adafruit_NeoPixel(N_LEDS, PIN, NEO_GRB + NEO_KHZ800);

void setup() {
  strip.begin();
}

int pos = START, dir = 1; // Position, direction of "eye"

void loop() {
  int j;

  // Draw 5 pixels centered on pos.  setPixelColor() will clip any
  // pixels off the ends of the strip, we don't need to watch for that.
  strip.setPixelColor(pos - 2, 0x100000); // Dark red
  strip.setPixelColor(pos - 1, 0x800000); // Medium red
  strip.setPixelColor(pos    , 0xFF3000); // Center pixel is brightest
  strip.setPixelColor(pos + 1, 0x800000); // Medium red
  strip.setPixelColor(pos + 2, 0x100000); // Dark red

  strip.show();
  delay(30);

  // Rather than being sneaky and erasing just the tail pixel,
  // it's easier to erase it all and draw a new one next time.
  for(j=-2; j<= 2; j++) strip.setPixelColor(pos+j, 0);

  // Bounce off ends of strip
  pos += dir;
  if(pos < START) {
    pos = START;
    dir = -dir;
  } else if(pos >= strip.numPixels() + START) {
    pos = strip.numPixels() + START - 2;
    dir = -dir;
  }
}