Fixing a flat - how to find the piercing object? Just had a flat and having problems finding the thing that pierced the tube in the tire. Normally I just run my fingers around in it, until I found it, but this time everything looks O.K.

My experience is though, if you do not find the object, another flat will happen soon ...

I know the trick with searching for the puncture on the tire in the same space where the hole is on the tube. I even flipped the tire so that the pattern is inside, but nothing to be found. 

It's a mountain bike tire, and the hole in the tube is very tiny.
The object that pierced the tire and tube may have been left behind or it might be embedded in the tire but hidden in the rubber. This can happen with small pieces of glass, wire, or thorns, especially in thicker treaded tires such as those found on a mountain bike. When the rubber of the tire is compressed against the ground the offending object will stick back out through the inside of the tire, re-puncturing the tube and then as that section of the tire loses contact with the ground the object conceals itself again. It's almost like a bee's stinger.

First thing I would do is just slap another tube in the tire. If you have another flat in the same place then you might have something still stuck in the tire that isn't immediately obvious. If you know how the tire was oriented against the tube, inspect both the inside and the outside of the tire around where you think the puncture occurred. Do it under bright light and look for small cuts in the tread. Use a pick or tweezers to dig around in any cuts you find to ensure that nothing is hiding in there. If you find something, great! Problem solved. If not it may be coincidence.

I'm also an advocate of patching the inside of tires after anything more than a pinhole puncture. If you have a cut that is more than a millimeter or two, you probably want to boot the tire. Otherwise you've got a weak spot where debris is more likely to penetrate the tire and pop another tube. You can buy tire boots, which are expensive, or you can use the glue type (not glueless) tube patches. I've had great success with tube patches on the inside of tires, even with road tires and mtb tubeless setups. Keep in mind that this wont work on cuts bigger than a few millimeters.