要解决Android后台服务计时器无法正常工作的问题，可以尝试以下方法：

1. 使用Handler和Runnable实现计时器：

public class MyService extends Service {
    private Handler handler;
    private Runnable runnable;
    private int interval = 1000; // 计时器间隔时间，单位毫秒
    private boolean isRunning = false;

    @Override
    public void onCreate() {
        super.onCreate();
        handler = new Handler();
        runnable = new Runnable() {
            @Override
            public void run() {
                // 在此处执行计时器任务
                Log.d("MyService", "Timer task executed");
                handler.postDelayed(this, interval);
            }
        };
    }

    @Override
    public int onStartCommand(Intent intent, int flags, int startId) {
        if (!isRunning) {
            handler.postDelayed(runnable, interval);
            isRunning = true;
        }
        return START_STICKY;
    }

    @Override
    public void onDestroy() {
        super.onDestroy();
        if (handler != null && runnable != null) {
            handler.removeCallbacks(runnable);
        }
        isRunning = false;
    }

    @Nullable
    @Override
    public IBinder onBind(Intent intent) {
        return null;
    }
}

2. 使用Timer和TimerTask实现计时器：

public class MyService extends Service {
    private Timer timer;
    private TimerTask timerTask;
    private int interval = 1000; // 计时器间隔时间，单位毫秒
    private boolean isRunning = false;

    @Override
    public void onCreate() {
        super.onCreate();
        timer = new Timer();
        timerTask = new TimerTask() {
            @Override
            public void run() {
                // 在此处执行计时器任务
                Log.d("MyService", "Timer task executed");
            }
        };
    }

    @Override
    public int onStartCommand(Intent intent, int flags, int startId) {
        if (!isRunning) {
            timer.schedule(timerTask, 0, interval);
            isRunning = true;
        }
        return START_STICKY;
    }

    @Override
    public void onDestroy() {
        super.onDestroy();
        if (timer != null) {
            timer.cancel();
        }
        isRunning = false;
    }

    @Nullable
    @Override
    public IBinder onBind(Intent intent) {
        return null;
    }
}

在AndroidManifest.xml中添加Service声明：

使用以上方法，可以在Service中实现后台计时器任务，并确保计时器正常工作。