I have actually experienced a tapping very similar to what you have described. For several years.
And the cause of this tapping would be shy in daylight, only manifest itself at night. It would also be shy if I looked in it's direction (i.e., when you look in its direction it would stop immediately). So, I eventually came to the conclusion that the cause of this tapping was not particularly strong or bold.
So, it's nothing to be afraid of, but I understand it can be annoying.
My best advice is to either ignore it, or if it's a bit too bothersome then you can take steps to stop what's causing it. For example, lighting a sandlewood incense in the area you meditate, while you are meditating may stop it. It may be as simple as that.
But if it's stubborn and you want to make it go away, this could take the help of a Buddhist monk or someone experienced with these things.
In my case I rarely hear the tapping anymore. But last year I had an experience for about six months with something that was doing much more than tapping! Much more bothersome. ;-) I eventually talked to some people in the know and took some rather gentle steps to cause it to cease. But I would have taken stronger steps had it not stopped pestering me.
I talked to several meditation masters and they told me these experiences are actually much more common than most people would think.
I don't want to say any more about this subject in this post, but I hope I have given you enough info to be of some value to you.
And regardless, stay with your meditation practice....don't stop it because of the tapping sounds.