Instead of uploading the .ino sketch (forcing us to download and open it externally), copy your code and include it in code tags in your post.
That way we can easily read your code along with your text and possibly catch any issues without downloading anything...
// A basic everyday NeoPixel strip test program.
// NEOPIXEL BEST PRACTICES for most reliable operation:
// - Add 1000 uF CAPACITOR between NeoPixel strip's + and - connections.
// - MINIMIZE WIRING LENGTH between microcontroller board and first pixel.
// - NeoPixel strip's DATA-IN should pass through a 300-500 OHM RESISTOR.
// - AVOID connecting NeoPixels on a LIVE CIRCUIT. If you must, ALWAYS
// connect GROUND (-) first, then +, then data.
// - When using a 3.3V microcontroller with a 5V-powered NeoPixel strip,
// a LOGIC-LEVEL CONVERTER on the data line is STRONGLY RECOMMENDED.
// (Skipping these may work OK on your workbench but can fail in the field)
#include <Adafruit_NeoPixel.h>
#define BUTTON_PIN 13 //trigger pull
// Which pin on the Arduino is connected to the NeoPixels?
// On a Trinket or Gemma we suggest changing this to 1:
#define LED_PIN 8
// How many NeoPixels are attached to the Arduino?
#define LED_COUNT 2
int a=0; //set int to 0 as base value
// Declare our NeoPixel strip object:
Adafruit_NeoPixel strip(LED_COUNT, LED_PIN, NEO_GRB + NEO_KHZ800);
// Argument 1 = Number of pixels in NeoPixel strip
// Argument 2 = Arduino pin number (most are valid)
// Argument 3 = Pixel type flags, add together as needed:
// NEO_KHZ800 800 KHz bitstream (most NeoPixel products w/WS2812 LEDs)
// NEO_KHZ400 400 KHz (classic 'v1' (not v2) FLORA pixels, WS2811 drivers)
// NEO_GRB Pixels are wired for GRB bitstream (most NeoPixel products)
// NEO_RGB Pixels are wired for RGB bitstream (v1 FLORA pixels, not v2)
// NEO_RGBW Pixels are wired for RGBW bitstream (NeoPixel RGBW products)
void setup() {
pinMode (13, INPUT); //trigger pin is input
strip.begin(); // INITIALIZE NeoPixel strip object (REQUIRED)
strip.show(); // Turn OFF all pixels ASAP
strip.setBrightness(50); // Set BRIGHTNESS to about 1/5 (max = 255)
}
void loop() {
digitalRead(BUTTON_PIN); //read trigger pin
if (BUTTON_PIN == HIGH) //if I pull trigger
{(int a=a; a<255; a++);
delay (500);} //int a (brightness) increases to a max of 255
else if (BUTTON_PIN == LOW)
{ (int a=a; a>=0; a--);
delay (500);} //when not pressed, brightness fades to zero
// Fill along the length of the strip in various colors...
// if (BUTTON_PIN == HIGH)
{ colorWipe(strip.Color(255, 0, 0), a); }// Red
// if (BUTTON_PIN == HIGH)
// {int a=a ; a<255 ; a++}
// else if (BUTTON_PIN == LOW)
// {int a=a ; a>=0 ; a--}
}
void colorWipe(uint32_t color, int wait) {
for(int i=0; i<strip.numPixels(); i++) { // For each pixel in strip...
strip.setPixelColor(i, color); // Set pixel's color (in RAM)
strip.show(); // Update strip to match
delay(wait); // Pause for a moment
}
}
Ive rewritten your code to get rid of delay(), see the exellent forum post regarding doing many things at once for reference.
I also added a more straightforward counter system, to add / subtract to/from the a-variable.
I really dont understand how the colorswipe function is working, but it appears as the a-value is the actual delay between color changes, not the actual color change itself.
If it were my project the neopixels would start with a cool color and gradually change to red (hot) while button is pressed, but its NOT my project, so i hope youre happy with the way my code works out for you. 
// A basic everyday NeoPixel strip test program.
// NEOPIXEL BEST PRACTICES for most reliable operation:
// - Add 1000 uF CAPACITOR between NeoPixel strip's + and - connections.
// - MINIMIZE WIRING LENGTH between microcontroller board and first pixel.
// - NeoPixel strip's DATA-IN should pass through a 300-500 OHM RESISTOR.
// - AVOID connecting NeoPixels on a LIVE CIRCUIT. If you must, ALWAYS
// connect GROUND (-) first, then +, then data.
// - When using a 3.3V microcontroller with a 5V-powered NeoPixel strip,
// a LOGIC-LEVEL CONVERTER on the data line is STRONGLY RECOMMENDED.
// (Skipping these may work OK on your workbench but can fail in the field)
#include <Adafruit_NeoPixel.h>
#define BUTTON_PIN 13 //trigger pull
// Which pin on the Arduino is connected to the NeoPixels?
// On a Trinket or Gemma we suggest changing this to 1:
#define LED_PIN 8
// How many NeoPixels are attached to the Arduino?
#define LED_COUNT 2
// old value int a=0; //set int to 0 as base value
// Declare our NeoPixel strip object:
Adafruit_NeoPixel strip(LED_COUNT, LED_PIN, NEO_GRB + NEO_KHZ800);
// Argument 1 = Number of pixels in NeoPixel strip
// Argument 2 = Arduino pin number (most are valid)
// Argument 3 = Pixel type flags, add together as needed:
// NEO_KHZ800 800 KHz bitstream (most NeoPixel products w/WS2812 LEDs)
// NEO_KHZ400 400 KHz (classic 'v1' (not v2) FLORA pixels, WS2811 drivers)
// NEO_GRB Pixels are wired for GRB bitstream (most NeoPixel products)
// NEO_RGB Pixels are wired for RGB bitstream (v1 FLORA pixels, not v2)
// NEO_RGBW Pixels are wired for RGBW bitstream (NeoPixel RGBW products)
// new code and variables:
uint32_t NOW = 0;
uint32_t lastUpdate = 0;
uint32_t lastCounterUpdate = 0;
uint32_t changeInterval = 500; // the interval for changing the color
uint8_t a = 0; //set int to 0 as base value, changed to unsigned int since you dont want negative values..
void checkElapsed(uint32_t timer,uint32_t limiter) {
return (NOW - timer >= limiter);
}
// end new code
void setup() {
pinMode (13, INPUT); //trigger pin is input
strip.begin(); // INITIALIZE NeoPixel strip object (REQUIRED)
strip.show(); // Turn OFF all pixels ASAP
strip.setBrightness(50); // Set BRIGHTNESS to about 1/5 (max = 255)
}
void loop() {
// digitalRead(BUTTON_PIN); //read trigger pin (but dont do anything with the read value??)
// new code
NOW = millis();
// if button is read inverted (pressed button counts down),
// change the "if (digitalRead(BUTTON_PIN))"" to "if (!digitalRead(BUTTON_PIN))"
if (digitalRead(BUTTON_PIN) { //if I pull trigger
if (checkElapsed(lastCounterUpdate,changeInterval)) {
lastCounterUpdate = NOW;
if (a < 255) {
a++;
}
}
colorWipe(strip.Color(255, 0, 0), a); // Red
}
else {
if (checkElapsed(lastCounterUpdate,changeInterval)) {
lastCounterUpdate = NOW;
if (a) {
a--;
}
}
}
}
// end new code
/* OLD code
if (BUTTON_PIN == HIGH) //if I pull trigger
{(int a=a; a<255; a++);
delay (500);} //int a (brightness) increases to a max of 255
else if (BUTTON_PIN == LOW)
{ (int a=a; a>=0; a--);
delay (500);} //when not pressed, brightness fades to zero
// Fill along the length of the strip in various colors...
// if (BUTTON_PIN == HIGH)
{ colorWipe(strip.Color(255, 0, 0), a); }// Red
// if (BUTTON_PIN == HIGH)
// {int a=a ; a<255 ; a++}
// else if (BUTTON_PIN == LOW)
// {int a=a ; a>=0 ; a--}
}
*/
void colorWipe(uint32_t color, int wait) {
for(int i=0; i<strip.numPixels(); i++) { // For each pixel in strip...
strip.setPixelColor(i, color); // Set pixel's color (in RAM)
strip.show(); // Update strip to match
delay(wait); // Pause for a moment
}
}
